Correction of birefringence in cubic crystalline optical systems

ABSTRACT

An optical system includes multiple cubic crystalline optical elements aligned along a common optical axis and having their crystal lattices oriented with respect to each other to minimize the effects of intrinsic birefringence and produce a system with reduced retardance. The optical system may be a refractive or catadioptric system having a high numerical aperture and using light with a wavelength at or below 248 nanometers. The net retardance of the system is less than the sum of the retardance contributions of the respective optical elements as the elements are oriented such that the intrinsic birefringences of the individual elements cancel each other out. In one embodiment, two [110] cubic crystalline optical elements are clocked with respect to one another and used in conjunction with a [100] cubic crystalline optical element to reduce retardance. Various birefringent elements, wave plates, and combinations thereof provide additional correction for residual retardance and wavefront aberrations. The optical system may be used in a photolithography tool to pattern substrates such as semiconductor substrates and thereby produce semiconductor devices.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This is a continuation application of U.S. patent applicationSer. No. 10/071,375, entitled CORRECTION OF BIREFRINGENCE IN CUBICCRYSTALLINE OPTICAL SYSTEMS, filed Feb. 7, 2002, and which claimspriority of U.S. Provisional Application Serial No. 60/295,212, entitledMEANS TO DETERMINE, CORRECT AND ADJUST FOR INTRINSIC BIREFRINGENCE INOPTICAL MATERIALS FOR USE IN LITHOGRAPHY LENSES, filed Jun. 1, 2001;U.S. Provisional Application Serial No. 60/296,694, entitled MEANS TODETERMINE, CORRECT AND ADJUST FOR INTRINSIC BIREFRINGENCE IN OPTICALMATERIALS FOR USE IN LITHOGRAPHY LENSES, filed Jun. 6, 2001; U.S.Provisional Application Serial No. 60/299,497, entitled CORRECTION OFINTRINSIC BIREFRINGENCE IN OPTICAL SYSTEMS USING CUBIC CRYSTALMATERIALS, filed Jun. 20, 2001; U.S. Provisional Application Serial No.60/299,603, entitled CORRECTION OF INDUCED BIREFRINGENCE IN CUBICCRYSTALS, filed Jun. 20, 2001; U.S. Provisional Application Serial No.60/335,093, entitled INTRINSIC BIREFRINGENCE COMPENSATION, filed Oct.30, 2001; and U.S. Provisional Application Serial No. 60/332,183,entitled COMPENSATION FOR INTRINSIC BIREFRINGENCE EFFECTS IN CUBICCRYSTALLINE OPTICAL SYSTEMS, filed Nov. 21, 2001, the contents of eachof which are herein incorporated by reference.

FIELD OF THE INVENTION

[0002] The present invention relates, most generally, to highperformance optical systems and lithography methods. More particularly,the present invention relates to an apparatus and method forcompensating for the effects of intrinsic birefringence in opticalsystems using cubic crystalline optical elements.

BACKGROUND OF THE INVENTION

[0003] In order to increase levels of device integration for integratedcircuit and other semiconductor devices, there is a drive to producedevice features having smaller and smaller dimensions. In today'srapidly advancing semiconductor manufacturing industry, there is arelated drive to produce such device features in a reliable andrepeatable manner.

[0004] Optical lithography systems are commonly used in the fabricationprocess to form images of device patterns upon semiconductor substrates.The resolving power of such systems is proportional to the exposurewavelength; therefore, it is advantageous to use exposure wavelengthsthat are as short as possible. For sub-micron lithography, deepultraviolet light having a wavelength of 248 nanometers or shorter iscommonly used. Wavelengths of interest include 193 and 157 nanometers.

[0005] At ultraviolet or deep ultraviolet wavelengths, the materialsused to form the lenses, windows, and other optical elements of thelithography system, are of critical significance. Such optical elementsmust be compatible with the short wavelength light used in theselithography systems.

[0006] Calcium fluoride and other cubic crystalline materials such asbarium fluoride, lithium fluoride, and strontium fluoride, representsome of the materials being developed is for use as optical elements for157 nanometer lithography, for example. These single crystal fluoridematerials have a desirably high transmittance compared to ordinaryoptical glass and can be produced with good homogeneity.

[0007] Accordingly, such cubic crystalline materials are useful asoptical elements in short wavelength optical systems such as wafersteppers and other projection printers used to produce small features onsubstrates such as semiconductor and other wafers used in thesemiconductor manufacturing industry. In particular, calcium fluoridefinds particular advantage in that it is an easily obtained cubiccrystalline material and large high purity single crystals can be grown.

[0008] A primary concern for the use of cubic crystalline materials foroptical elements in deep ultraviolet lithography systems is anisotropyof refractive index inherent in cubic crystalline materials; this isreferred to as “intrinsic birefringence.” It has been recently reported[J. Burnett, Z. H. Levine, and E. Shipley, “Intrinsic Birefringence in157 nm materials,” Proc. 2^(nd) Intl. Symp on 157 nm Lithography,Austin, Intl SEMATEC, ed. R. Harbison, 2001] that cubic crystallinematerials such as calcium fluoride, exhibit intrinsic birefringence thatscales as the inverse of the square of the wavelength of light used inthe optical system. The magnitude of this birefringence becomesespecially significant when the optical wavelength is decreased below250 nanometers and particularly as it approaches 100 nanometers. Ofparticular interest is the effect of intrinsic birefringence at thewavelength of 157 nanometers (nm), the wavelength of light produced byan F₂ excimer laser favored in the semiconductor manufacturing industry.

[0009] Birefringence, or double-refraction, is a property of refractivematerials in which the index of refraction is anisotropic. For lightpropagating through a birefringent material, the refractive index variesas a function of polarization and orientation of the material withrespect to the propagation direction. Unpolarized light propagatingthrough a birefringent material will generally separate into two beamswith orthogonal polarization states.

[0010] When light passes through a unit length of a birefringentmaterial, the difference in refractive index for the two ray paths willresult in an optical path difference or retardance. Birefringence is aunitless quantity, although it is common practice in the lithographycommunity to express it in units of nm/cm. Birefringence is a materialproperty, while retardance is an optical delay between polarizationstates. The retardance for a given ray through an optical system may beexpressed in nm, or it may be expressed in terms of number of waves of aparticular wavelength.

[0011] In uniaxial crystals, such as magnesium fluoride or crystalquartz, the direction through the birefringent material in which the tworefracted beams travel with the same velocity is referred to as thebirefringence axis. The term optic axis is commonly used interchangeablywith birefringence axis when dealing with single crystals. In systems oflens elements, the term optical axis usually refers to the symmetry axisof the lens system. To avoid confusion, the term optical axis will beused hereinafter only to refer to the symmetry axis in a lens system.For directions through the material other than the birefringence axis,the two refracted beams will travel with different velocities. For agiven incident ray upon a birefringent medium, the two refracted raysare commonly described as the ordinary and extraordinary rays. Theordinary ray is polarized perpendicular to the birefringence axis andrefracts according to Snell's Law, and the extraordinary ray ispolarized perpendicular to the ordinary ray and refracts at an anglethat depends on the direction of the birefringence axis relative to theincident ray and the amount of birefringence. In uniaxial crystals, thebirefringence axis is oriented along a single direction, and themagnitude of the birefringence is constant throughout the material.Uniaxial crystals are commonly used for optical components such asretardation plates and polarizers.

[0012] In contrast, however, cubic crystals have been shown to have botha birefringence axis orientation and magnitude that vary depending onthe propagation direction of the light with respect to the orientationof the crystal lattice. In addition to birefringence, which is thedifference in the index of refraction seen by the twoeigenpolarizations, the average index of refraction also varies as afunction of angle of incidence, which produces polarization independentphase errors.

[0013] Crystal axis directions and planes are described herein usingMiller indices, which are integers with no common factors and that areinversely proportional to the intercepts of the crystal planes along thecrystal axes. Lattice planes are given by the Miller indices inparentheses, e.g. (100), and axis directions in the direct lattice aregiven in square brackets, e.g. [111]. The crystal lattice direction,e.g. [111], may also be referred to as the [111] crystal axis of thematerial or optical element. The (100), (010), and (001) planes areequivalent in a cubic crystal and are collectively referred to as the{100} planes. For example, light propagating through an exemplary cubiccrystalline optical element along the [110] crystal axis experiences themaximum birefringence, while light propagating along the [100] crystalaxis experiences no birefringence.

[0014] Thus, as a wavefront propagates through an optical elementconstructed from a cubic crystalline material, the wavefront may beretarded because of the intrinsic birefringence of the optical element.The retardance magnitude and orientation may each vary, because thelocal propagation angle through the material varies across thewavefront. Such variations may be referred to as “retardanceaberrations.” Retardance aberrations split a uniformly polarizedwavefront into two wavefronts with orthogonal polarizations. Each of theorthogonal wavefronts will experience a different refractive index,resulting in different wavefront aberrations. These aberrations arecapable of significantly degrading image resolution and introducingdistortion of the image field at the wavelengths of interest, such as157 nm, particularly for sub-micron projection lithography insemiconductor manufacturing. It can be therefore seen that there is aneed in the art to compensate for wavefront aberrations caused byintrinsic birefringence of cubic crystalline optical elements, which cancause degradation of image resolution and image field distortion,particularly in projection lithography systems using light havingwavelengths in the deep ultraviolet range.

SUMMARY OF THE INVENTION

[0015] To address these and other needs, and in view of its purposes,the present invention provides a method and apparatus for preventingintrinsic birefringence in cubic crystalline optical systems fromcausing wavefront aberrations. The crystal axes of the cubic crystallinelens elements are oriented to minimize net retardance by balancing theretardance contributions from the individual lens elements.

[0016] In one exemplary embodiment, the present invention provides anoptical system which includes a projection lens formed of a plurality ofoptical elements, two or more of which are constructed from cubiccrystalline material and oriented with their [110] cubic crystallinelattice direction along the system optical axis and with relativerotations about the optical axis to give reduced retardance for lightpropagating at small angles relative to the system optical axis, and oneor more elements oriented with the optical axis substantially along the[100] cubic crystalline lattice direction to give reduced retardance foroff-axis light propagating at larger angles with respect to the systemoptical axis.

[0017] In another exemplary embodiment, the present invention providesan optical system which includes four optical elements which areconstructed from cubic crystalline material and oriented with theoptical axis substantially along their [110] cubic crystalline latticedirections. The optical elements are oriented about the optical axis togive reduced retardance for light propagating at small angles relativeto the system optical axis. The system further includes an opticalelement oriented with its [100] crystal lattice direction substantiallyalong the optical axis to give reduced retardance for light propagatingat larger angles with respect to the system optical axis.

[0018] In another exemplary embodiment, the present invention providesan optical system that includes a plurality of optical elements, two ormore of which are constructed from cubic crystalline material andoriented with their [110] cubic crystalline lattice direction along theoptical axis of the system, and with relative rotations about theoptical axis to give reduced retardance for light propagating at smallangles relative to the [110] lattice direction. A stress-inducedbirefringence is applied to either a [110] cubic crystal optical elementor a further optical element such as a non-cubic crystalline element ora [100] optical element, to reduce residual retardance of the opticalsystem.

[0019] In another exemplary embodiment, the present invention provides amethod and apparatus for reducing retardance aberrations caused byintrinsic birefringence by providing a lens system, orienting two ormore elements with the optical axis substantially along the [110] cubiccrystalline lattice directions of the elements and one or more elementswith the optical axis substantially along the [100] cubic crystallinelattice directions of the elements, and providing optimized relativerotations of the elements about the optical axis.

[0020] In another exemplary embodiment, the present invention provides amethod and apparatus for reducing retardance aberrations caused byintrinsic birefringence by providing a lens system defined by a lensprescription, then splitting at least one of the elements of the lenssystem into multiple cubic crystalline components, oriented to reduceretardance aberrations while maintaining the overall element dimensionsdefined by the lens prescription.

[0021] In yet another exemplary embodiment, the present inventionprovides a method and apparatus for reducing retardance caused byintrinsic birefringence by providing a lens system with at least twocubic crystalline optical elements and providing a stress-inducedbirefringence to at least one of the optical elements to reduce residualretardance variations.

[0022] Another aspect of the present invention is an apparatus andmethod for compensating for residual astigmatism due to variations inthe average index of refraction in the cubic crystalline opticalelements, through the use of at least one optical element whose baseradius of curvature differs in orthogonal directions.

[0023] In another exemplary embodiment, the present invention provides aphotolithography tool including one of the above-described opticalsystems.

[0024] In another exemplary embodiment, the present invention provides amethod and apparatus for using the selectively oriented crystalline lenselements to form semiconductor devices on semiconductor substrates usedin the semiconductor manufacturing industry.

[0025] In another exemplary embodiment, the present invention provides asemiconductor device formed using a lithography tool including theselectively oriented cubic crystalline lens elements.

BRIEF DESCRIPTION OF THE DRAWING

[0026] The present invention is best understood from the followingdetailed description when read in conjunction with the accompanyingdrawing. It is emphasized that, according to common practice, thevarious features of the drawing are not to scale. On the contrary, thedimensions of the various features are arbitrarily expanded or reducedfor clarity. Included in the drawing are the following figures:

[0027]FIG. 1 is a schematic illustration of the projection optics of anexemplary lithography system;

[0028]FIG. 2 is a schematic illustration of an exemplary lithographysystem;

[0029]FIG. 3A is a graphical representation of variation ofbirefringence axis orientation with respect to a cubic crystal lattice;

[0030]FIG. 3B is a graphical representation of variation ofbirefringence magnitude with respect to a cubic crystal lattice;

[0031]FIG. 4 is a perspective view showing angular relationships betweenvarious directions through an exemplary cubic crystalline lattice;

[0032]FIG. 5A is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [110] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

[0033]FIG. 5B is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [100] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

[0034]FIG. 5C is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [111] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

[0035]FIG. 6 is a schematic illustration of an exemplary optical systemwith three cubic crystalline elements concentric about the focal pointof a converging beam;

[0036]FIG. 7A is a graphical illustration of net retardance magnitudeand orientation across the pupil for an exemplary embodiment of theoptical system depicted in FIG. 6 in which the optical axis extendsalong the [110] lattice direction for each element and the crystal axesfor all elements are oriented identically;

[0037]FIG. 7B is a graphical illustration of net retardance magnitudeand orientation across the pupil for an exemplary embodiment of theoptical system depicted in FIG. 6 in which the optical axis extendsalong the [100] lattice direction for each element and the crystal axesfor all elements are oriented identically;

[0038]FIG. 7C is a graphical illustration of net retardance magnitudeand orientation across the pupil for an exemplary embodiment of theoptical system depicted in FIG. 6 in which the optical axis extendsalong the [111] lattice direction for each element and the crystal axesfor all elements are oriented identically;

[0039]FIG. 8A is a graphical illustration showing the individualcontribution to the retardance across the pupil for the first element ofthe optical system depicted in FIG. 6, in which the first element is a[110] optical element and is rotated about the optical axis such thathorizontally oriented retardance is produced along the optical axis;

[0040]FIG. 8B is a graphical illustration showing the individualcontribution to the retardance across the pupil for the second elementof the optical system depicted in FIG. 6, in which the second element isa [110] optical element and is rotated about the optical axis such thatvertically oriented retardance is produced along the optical axis;

[0041]FIG. 8C is a graphical illustration showing the individualcontribution to the retardance across the pupil for the third element ofthe optical system depicted in FIG. 6, in which the third element is a[100] optical element and is rotated about the optical axis such thatthe peak retardance is oriented along the pupil diagonals;

[0042]FIG. 9A is a graphical illustration showing the combinedretardance across the pupil for the first and second elements of theoptical system depicted in FIG. 6 according to the exemplary embodimentin which the first two elements are [110] cubic crystalline opticalelements and the third element is a [100] cubic crystalline opticalelement;

[0043]FIG. 9B is a graphical illustration showing the net retardanceacross the pupil for the optical system depicted in FIG. 6 according tothe exemplary embodiment in which the first two elements are [110] cubiccrystalline optical elements and the third element is a [100] cubiccrystalline optical element;

[0044]FIG. 9C is a graphical illustration showing the net retardanceacross the pupil for an optical system depicted in FIG. 6 according toanother exemplary embodiment in which the first two elements are [110]cubic crystalline optical elements and the third element is a [100]cubic crystalline optical element and in which the third elementincludes a thickness selected to minimize the net RMS retardance;

[0045]FIG. 9D is a graphical illustration plotting the radial retardancevariation across the first element in the optical system depicted inFIG. 6, when a compressive hoop stress is applied around the perimeterof the first element;

[0046]FIG. 9E is a graphical illustration showing the individualcontribution to the retardance across the pupil for the first element ofthe optical system depicted in FIG. 6, when an exemplary tensile hoopstress is applied around the perimeter of the element, and withoutincluding the retardance caused by intrinsic birefringence;

[0047]FIG. 9F is a graphical illustration showing the net retardanceacross the pupil for the optical system depicted in FIG. 6, when anexemplary tensile hoop stress is applied around the perimeter of thefirst element to minimize the net RMS retardance;

[0048]FIG. 10 is a schematic illustration showing an exemplary opticalsystem with five cubic crystalline elements concentric about the focalpoint of a converging beam;

[0049]FIG. 11A is a graphical illustration showing net retardancemagnitude and orientation across the pupil for an exemplary embodimentof the optical system depicted in FIG. 10 in which the optical axis isalong the [110] lattice direction for each element and the crystal axesfor all elements are oriented identically;

[0050]FIG. 11B is a graphical illustration showing net retardancemagnitude and orientation across the pupil for an exemplary embodimentof the optical system depicted in FIG. 10 in which the optical axis isalong the [100] lattice direction for each element and the crystal axesfor all elements are oriented identically;

[0051]FIG. 11C is a graphical illustration showing net retardancemagnitude and orientation across the pupil for an exemplary embodimentof the optical system depicted in FIG. 10 in which the optical axis isalong the [111] lattice direction for each element and the crystal axesfor all elements are oriented identically;

[0052] FIGS. 12A-14C are each graphical illustrations showing retardancemagnitude and orientation for the optical system shown in FIG. 10, inwhich the first four elements are [110] cubic crystalline opticalelements and the fifth element is a [100] cubic crystalline opticalelement: FIG. 12A shows the individual contribution to the retardanceacross the pupil for the first element, in which the retardance alongthe optical axis is rotated by 17.632° with respect to horizontal;

[0053]FIG. 12B shows the individual contribution to the retardanceacross the pupil for the second element, in which the retardance alongthe optical axis is rotated by −17.632° with respect to horizontal;

[0054]FIG. 12C shows the individual contribution to the retardanceacross the pupil for the third element, in which the retardance alongthe optical axis is rotated by 72.368° with respect to horizontal;

[0055]FIG. 12D shows the individual contribution to the retardanceacross the pupil for the fourth element, in which the retardance alongthe optical axis is rotated by −72.368° with respect to horizontal;

[0056]FIG. 13A shows the retardance across the pupil for the first andthird elements overlapping one another;

[0057]FIG. 13B shows the net retardance across the pupil for the firstand third elements;

[0058]FIG. 13C shows the net retardance across the pupil for the secondand fourth elements;

[0059]FIG. 14A shows the net retardance across the pupil for the firstfour elements;

[0060]FIG. 14B shows the individual contribution to the retardanceacross the pupil for the fifth element;

[0061]FIG. 14C shows the net retardance across the pupil;

[0062]FIG. 15 is a schematic illustration of an exemplary large format,refractive projection lens;

[0063]FIGS. 16A and 16B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 15 at centraland extreme field points, respectively, due to single-layeranti-reflection coatings;

[0064]FIGS. 17A and 17B are graphical illustrations showingdiattenuation across the pupil for the exemplary lens depicted in FIG.15 at central and extreme field points, respectively, due tosingle-layer anti-reflection coatings;

[0065]FIGS. 18A, 18B, 18C, and 18D are contour plots showing theresidual wavefront error for the exemplary lens depicted in FIG. 15:FIG. 18A shows the wavefront error for an input polarization in the Xdirection used with an exit pupil analyzer in the X direction for thecentral field point. FIG. 18B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 18C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 18Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

[0066]FIGS. 19A and 19B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 15 at centraland extreme field points, respectively, in which all elements are cubiccrystals identically aligned in three dimensions, with the optical axisextending along the [110] crystal lattice direction and a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

[0067]FIGS. 20A and 20B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 15 at centraland extreme field points, respectively, in which all elements are cubiccrystals identically aligned in three dimensions, with the optical axisextending along the [100] crystal lattice direction and a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

[0068]FIGS. 21A and 21B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 15 at centraland extreme field points, respectively, in which all elements are cubiccrystals identically aligned in three dimensions, with the optical axisextending along the [111] crystal lattice direction and a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

[0069]FIG. 22 is a schematic illustration showing the exemplary lensdepicted in FIG. 15, with the crystal axes of the elements selected andoriented to compensate for intrinsic birefringence, in which the hatchedelements are [100] cubic crystalline optical elements and all others are[110] cubic crystal optical elements;

[0070]FIGS. 23A and 23B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 22 at centraland extreme field points, respectively, due to anti-reflection coatingsand intrinsic birefringence of all elements;

[0071]FIGS. 24A, 24B, 24C, and 24D are contour plots showing theresidual wavefront error for the exemplary lens depicted in FIG. 22.FIG. 24A shows the wavefront error for an input polarization in the Xdirection used with an exit pupil analyzer in the X direction for thecentral field point. FIG. 24B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 24C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 24Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

[0072]FIGS. 25A and 25B are graphical illustrations showing retardanceacross the pupil for the exemplary lens shown in FIG. 1 at central andextreme field points, respectively due to single-layer anti-reflectioncoatings;

[0073]FIGS. 26A and 26B are graphical illustrations showingdiattenuation across the pupil for the exemplary lens depicted in FIG. 1at central and extreme field points, respectively due to single-layeranti-reflection coatings;

[0074]FIGS. 27A, 27B, 27C, and 27D are contour plots showing theresidual wavefront error for the exemplary lens depicted in FIG. 1. FIG.27A shows the wavefront error for an input polarization in the Xdirection used with an exit pupil analyzer in the X direction for thecentral field point. FIG. 27B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 27C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 27Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

[0075]FIGS. 28A and 28B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 1 at centraland extreme field points, respectively, in which all elements areidentically aligned in three dimensions, with their [110] crystallattice direction along the optical axis and including a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

[0076]FIGS. 29A and 29B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 1 at centraland extreme field points, respectively, in which all elements areidentically aligned in three dimensions, with their [100] crystallattice direction along the optical axis and including a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

[0077]FIGS. 30A and 30B are graphical illustrations showing retardanceacross the pupil for the lens depicted in FIG. 1 at central and extremefield points, respectively, in which all elements are identicallyaligned in three dimensions, with their [111] crystal lattice directionalong the optical axis and including a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

[0078]FIG. 31 is a schematic illustration showing the exemplary lensdepicted in FIG. 1 with the last two elements split into two segmentswith different relative rotations about the optical axis and the crystalaxes of the elements oriented to compensate for intrinsic birefringence,in which the hatched elements have their [100] crystal lattice directionalong the optical axis and all others are oriented along with their[110] crystal lattice direction along the optical axis;

[0079]FIGS. 32A and 32B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 31 at centraland extreme field points, respectively, due to anti-reflection coatingsand intrinsic birefringence of all elements;

[0080]FIGS. 33A, 33B, 33C, and 33D are contour plots showing theresidual wavefront error for the exemplary lens depicted in FIG. 31.FIG. 33A shows the wavefront error for an input polarization in the Xdirection used with an exit pupil analyzer in the X direction for thecentral field point. FIG. 33B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 33C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 33Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

[0081]FIG. 34 is a schematic illustration showing an exemplary largeformat, catadioptric projection lens;

[0082]FIGS. 35A and 35B are graphical illustrations showing retardanceacross the pupil for the lens depicted in FIG. 34 at central and extremefield points, respectively due to single-layer anti-reflection coatings;

[0083]FIGS. 36A, 36B, 36C, and 36D are contour plots showing theresidual wavefront error for the lens depicted in FIG. 34. FIG. 36Ashows the wavefront error for an input polarization in the X directionused with an exit pupil analyzer in the X direction for the centralfield point. FIG. 36B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 36C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 36Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

[0084]FIGS. 37A and 37B are graphical illustrations showing retardanceacross the pupil for the lens depicted in FIG. 34 at central and extremefield points, respectively, in an exemplary embodiment in which allelements between the second wave plate and the image plane areidentically aligned in three dimensions, with the optical axis along the[110] crystal lattice direction and a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

[0085]FIGS. 38A and 38B are graphical illustrations showing retardanceacross the pupil for the lens depicted in FIG. 34 at central and extremefield points, respectively, in an exemplary embodiment in which allelements between the second wave plate and the image plane areidentically aligned in three dimensions, with the optical axis along the[100] crystal lattice direction and a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

[0086]FIGS. 39A and 39B are graphical illustrations showing retardanceacross the pupil for the lens depicted in FIG. 34 at central and extremefield points, respectively, in an exemplary embodiment in which allelements between the second wave plate and the image plane areidentically aligned in three dimensions, with the optical axis along the[111] crystal lattice direction and a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

[0087]FIG. 40 is a schematic illustration of the exemplary lens shown inFIG. 34 with the last element of FIG. 34 split into two sub-elements, inwhich the hatched elements are [110] cubic crystalline optical elements,and all others are [100] cubic crystalline optical elements;

[0088]FIGS. 41A and 41B are graphical illustrations showing retardanceacross the pupil for the exemplary lens depicted in FIG. 40 at centraland extreme field points, respectively, due to anti-reflection coatingsand the intrinsic birefringence of the front six elements, with thecrystal lattice orientation of the front six elements chosen to minimizethe variation in the retardance along horizontal and verticaldirections;

[0089]FIGS. 42A and 42B are graphical illustrations showing retardanceacross the pupil for the lens depicted in FIG. 40 at central and extremefield points, respectively, due to anti-reflection coatings andintrinsic birefringence of the group of elements between the second waveplate and the image plane;

[0090]FIGS. 43A and 43B are graphical illustrations showing retardanceacross the pupil for the lens depicted in FIG. 40 at central and extremefield points, respectively, due to anti-reflection coatings andintrinsic birefringence of all elements;

[0091]FIGS. 44A, 44B, 44C, and 44D are contour plots showing theresidual wavefront error for the lens depicted in FIG. 40. FIG. 44Ashows the wavefront error for an input polarization in the X directionused with an exit pupil analyzer in the X direction for the centralfield point. FIG. 44B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 44C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 44Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

[0092]FIG. 45 is a schematic illustration of an exemplary optical systemwith two cubic crystalline elements concentric about the focal point ofa converging beam;

[0093]FIG. 46A is a graphical illustration showing the individualcontribution to the retardance across the pupil for the first element ofthe optical system depicted in FIG. 45, when an exemplary compressivehoop stress is applied around the perimeter of the element, withoutincluding the retardance caused by intrinsic birefringence; and

[0094]FIG. 46B is a graphical illustration showing the net retardanceacross the pupil for the optical system depicted in FIG. 45, when anexemplary compressive hoop stress is applied around the perimeter of theelement to minimize the net RMS retardance.

DETAILED DESCRIPTION OF THE INVENTION

[0095] It is known in the art that cubic crystalline materials favoredin high performance lithography systems, such as the photolithographictools used in the semiconductor manufacturing industry, exhibitintrinsic birefringence, i.e., an inherent anisotropy in refractiveindex. When used for construction of elements of an optical system, thebirefringent properties of these cubic crystalline materials may producewavefront aberrations that significantly degrade image resolution andintroduce field distortion. This is especially true for the demandingresolution and overlay requirements in today's semiconductormanufacturing industry, which emphasizes increased levels of integrationand reduced feature sizes.

[0096] The present invention utilizes the concept that both thebirefringence direction and magnitude can be determined for a cubiccrystalline material and that optical elements may be formed and alignedto balance, or compensate for, the retardance aberrations caused by theintrinsic birefringence contributions of the individual elements. Forexample, the intrinsic birefringence variation within thethree-dimensional lattice orientation can be determined for thesematerials. Furthermore, when a plurality of cubic crystalline opticalelements is aligned such that each of the optical elements has aspecified three-dimensional lattice orientation with respect to a commonoptical axis, the plurality of aligned optical elements will have a netretardance that varies in a known manner.

[0097] This invention relates to a technique to compensate for theeffects of intrinsic birefringence in optical systems employing cubiccrystalline optical elements. The compensation is achieved throughproper selection of the crystal axis directions of the individualoptical elements and is applicable to optical systems using polarized orunpolarized radiation. In one exemplary embodiment, the compensation maybe achieved by utilizing a sufficient number of cubic crystallineoptical elements with the optical axis along their [110] crystal latticedirection. The invention also provides for compensating for residualastigmatism due to variations in the average index of refraction invarious exemplary cubic crystalline optical systems. In one exemplaryembodiment, this compensation may be achieved by varying the base radiusof curvature of at least one optical element, in orthogonal directions.

[0098] The various exemplary cubic crystalline optical systems andmethods for forming aberration-free patterns on semiconductor substratesare particularly advantageous as feature sizes become increasinglysmaller and approach the half wavelength of the light used to producethe patterns. Such techniques find particular advantage in highnumerical aperture (NA) lens systems but the various aspects of thepresent invention find application in optical systems having bothrelatively high and relatively low numerical apertures.

[0099]FIG. 1 is a schematic illustration showing an exemplary projectionoptics section of an exemplary lithography system. The optical systemshown in FIG. 1 is substantially similar to the optical system shown anddescribed in the seventh embodiment of European Patent EP 1 139 138 A1,issued to K. Omura on Apr. 10, 2001, the contents of which are hereinincorporated by reference. The exemplary optical system may be a largeformat refractive projection lens operating at an NA of 0.75, a peakwavelength of 193.3 nm and 4×reduction. Such an optical system isintended to be exemplary only and other optical systems may be used inother exemplary embodiments. Exemplary optical system 2 may be theprojection optics section of a lithography tool 4 in an exemplaryembodiment. In the exemplary embodiment, optical system 2 is aprojection lens disposed between exemplary reticle 6 and substrate 12.Reticle 6 may be considered to include the object field with the imagefield formed on substrate 12.

[0100] Optical system 2 is a lens system, commonly referred tocollectively as a “lens,” composed of a plurality of individual lenselements L, optical axis 10, and aperture stop (AS) 9. Reticle 6includes a mask pattern which is to be projected onto surface 13 ofsubstrate 12. According to an exemplary embodiment, substrate 12 may bea semiconductor wafer used in the semiconductor manufacturing industry,and surface 13 may be coated with a photosensitive material, such as aphotoresist commonly used in the semiconductor manufacturing industry.Other substrates may be used according to other exemplary embodiments.According to other exemplary embodiments within various microlithographytools, reticle 6 may be a photomask. Generally speaking, the reticle orphotomask, hereinafter referred to collectively as reticle 6, is amedium which includes a pattern of clear and opaque sections that formthe object field. Light is projected through the pattern and the patternis projected through the lens system and onto surface 13 of substrate12. The pattern projected from the reticle 6 onto substrate surface 13may be uniformly reduced in size to various degrees such as 10:1, 5:1,4:1 or others, according to the various exemplary embodiments. Theexemplary system may include a numerical aperture, NA, of 0.75, butsystems having other numerical apertures, such as within the range of0.60 to 0.90, may be used alternatively.

[0101] The arrangement of the plurality of lens elements L, is intendedto be exemplary only and various other arrangements of individual lenselements having various shapes may be used according to other exemplaryembodiments. The element thicknesses, spacings, radii of curvature,aspheric coefficients, and the like, are considered to be the lensprescription. The lens system or “lens” of the present invention ispreferably formed of a plurality of individual lens elements L, one ormore of which may be constructed with cubic crystalline material. Cubiccrystalline materials such as strontium fluoride, barium fluoride,lithium fluoride, and calcium fluoride may be used. Calcium fluoride isthe preferred material. In an exemplary embodiment, each of the cubiccrystalline optical elements will be formed of the same cubiccrystalline material. The lens may include lens elements L which areformed of non-cubic crystalline material such as low-OH fused silica,also known as dry fused silica. Each of the individual lens elements, L,is arranged along a common optical axis 10. In the exemplary embodiment,optical axis 10 is linear.

[0102]FIG. 2 is a schematic illustration showing optical system 2functioning as the projection optics section within lithography tool 4.FIG. 2 shows optical source 8 and substrate 12. Reticle 6 is disposedbetween condenser optics 14 and projection optics 2 and includes thepattern to be projected onto substrate 12. The optical field of reticle6 may be of various dimensions. Each of projection optics 2 andcondenser optics 14 may include an aperture stop and a plurality of lenselements, windows, and other refractive and reflective members. Theoptical system shown in FIG. 2 includes linear optical axis 10 andlithography tool 4 may be a wafer stepper, projection printer, or otherphotolithography or microlithography tool used in the semiconductorindustry. Lithography tool 4 may likewise be a scanning optical system,a step-and-repeat optical system or other microlithography or projectionoptics system. In a scanning-type optical system, a pattern on reticle 6is projected and scanned onto corresponding sections of surface 13 ofsubstrate 12. In a step-and-repeat optical system, such as aconventional wafer stepper, the pattern on reticle 6, is projected ontomultiple different portions of surface 13 in a plurality of discreteoperations. Reticle 6 is considered to be at the object field oflithography tool 4, while substrate 12 is considered to be at the imagefield of lithography tool 4. The reticle pattern includes various fieldpoints which are projected onto surface 13 simultaneously.

[0103] In an exemplary embodiment, the pattern printed on reticle 6 willbe used to create a circuit pattern on surface 13 for an integratedcircuit device being formed on substrate 12. According to an exemplaryembodiment, the pattern may be projected onto a photosensitive materialformed on surface 13 to form an exposure pattern. The exposure patternmay be developed using conventional means, to produce a photo pattern inthe photosensitive material. The photo pattern may be translated intothe substrate by etching or other means. According to other exemplaryembodiments, substrate 12 may include a series of layers of materialsformed thereon. In this embodiment, surface 13 may be one of the layersand the photo pattern formed on the layer. Etching or other means may beused to translate the photo pattern into the layer. Similarly-formedphoto patterns may be used to enable spatially selective doping usingknown methods such as ion implantation. In this manner, multiplephotolithographic operations using the techniques of the presentinvention, may be used to form various circuit patterns in variouslayers to create a completed semiconductor device such as an integratedcircuit. An advantage of the present invention is that images formed onthe substrate have sufficiently low aberration to enable preciselydimensioned and aligned device features to be formed having reducedsizes.

[0104] In an exemplary scanning optical system, the optical field ofreticle 6 which is projected and scanned onto the substrate surface mayhave a height of 26 millimeters and a width of a few millimeters. Otherfield dimensions may be used according to other exemplary embodimentsand depending on the type of lithography tool in which the projectionoptics are included.

[0105] Optical source 8 produces a light that is subsequently shaped andconditioned by condenser lens 14. The optical wavelength of source 8 mayvary, and may be no greater than 248 nanometers in an exemplaryembodiment. In one exemplary embodiment, light having a wavelength ofabout 157 nanometers may be used. In an exemplary embodiment, opticalsource 8 may produce linearly polarized light. One optical source whichproduces linearly polarized light is an excimer laser. According toother exemplary embodiments, optical source 8 may produce light which isnon-polarized. According to various exemplary embodiments, a KrF excimerlaser operating at about 248 nm, an ArF excimer laser operating at about193 nm, or an F₂ excimer laser operating at about 157 nm, may be used asoptical source 8.

[0106] The light produced by the optical source, shaped and conditionedby the condenser lens and used to project an image from the reticle orphotomask onto the substrate, may be described as a light beam comprisedof a plurality of rays. Light rays emanating from an individual objectfield point on the reticle or photomask form a wavefront that isprojected by the projection lens to a corresponding image field point atthe substrate. The chief ray is the ray from a given field point thatpasses through the center of the aperture stop and system pupils. For anobject field point located where the optical axis intersects thereticle, the chief ray travels along the optical axis. The full imagefield is therefore generated by a plurality of wavefronts.

[0107] Although described in conjunction with a lithography tool used topattern substrates in the semiconductor industry, the various exemplaryoptical systems of the present invention are useful in any applicationin which a pattern is projected through an optical system, onto asubstrate.

[0108]FIG. 3A is a three dimensional vector plot showing the spatialvariation in birefringence axis orientation within a material having acubic crystalline lattice. The cubic crystalline lattice may be that ofcalcium fluoride, in one embodiment. FIG. 3B is a 3-D plot correspondingto a quadrant of the vector plot shown in FIG. 3A, and showing thecorresponding magnitude of the intrinsic birefringence. It can be seenthat the localized magnitude and axis of the birefringence varyspatially throughout the crystal in a known fashion. It can also be seenthat, depending on the direction along which light travels through sucha cubic crystalline material, the birefringence magnitude and theorientation of the birefringence axis relative to the direction ofpropagation will vary. FIG. 3B represents an octant of the crystallattice: the extension of this diagram to all possible directionsthrough the crystal gives twelve directions for maximum birefringence,or birefringence lobes.

[0109] The crystal axis directions shown in FIGS. 3A and 3B aredescribed using Miller indices, which are integers with no commonfactors that are inversely proportional to the intercepts of the crystalplanes along the crystal axes. Lattice planes are given by the Millerindices in parentheses, e.g. (101), and axis directions in the crystallattice are given in square brackets, e.g. [111]. The crystal latticedirection, e.g. [110], may also be referred to as the [110] crystal axisof the element or material, and a cubic crystalline optical elementarranged with its [110] crystal axis along the system optical axis, maybe referred to as a [110] optical element. The (100), (010), and (001)planes are equivalent in a cubic crystal and are collectively referredto as the {100} planes.

[0110] The crystalline material can therefore be advantageously cutalong a given plane and arranged such that light normal to that planetravels along a chosen axis direction. For example, light travelingalong the [100] crystal axis 18 (i.e. along the [100] crystal latticedirection), which is oriented normal to the (100) crystal lattice plane16, sees a fixed and deterministic localized intrinsic birefringence.The birefringence magnitude and birefringence axis direction encounteredby a given ray therefore varies as a function of the direction alongwhich the light ray travels through the crystal.

[0111]FIG. 4 is a perspective view showing angular relationships betweenvarious directions through an exemplary cubic crystalline lattice. Thecubic crystalline lattice may be that of calcium fluoride, for example.FIG. 4 includes peak intrinsic birefringence directions along the [101],[110], and [011] lattice directions, indicated by lines 22, 24, and 26,respectively. Line 20 represents the [111] crystal axis direction, whichcorresponds to a direction through the crystal without intrinsicbirefringence.

[0112]FIGS. 5A, 5B, and 5C are schematic representations of thevariations in birefringence magnitude and birefringence axis orientationin angular space for optical axis orientations along the [110], [100],and [111] lattice directions, respectively, for the cubic crystallinelattice structure shown in FIG. 4. The center of the plot represents thebirefringence encountered by a ray traveling along the indicated crystalaxis and normal to the plane of the illustration. Birefringence depictedat increased radial distance from the center represents thebirefringence for rays at increased angles of propagation with respectto the optical axis. In each of FIGS. 5A-5C, the localized birefringenceaxis is indicated by the direction of lines plotted on a square grid,and the magnitude is indicated by the relative length of the lines.

[0113] The variation of birefringence magnitude in FIGS. 5A-5C ischaracterized by several lobes, also referred to as nodes, distributedazimuthally in which the birefringence is maximized. Each of FIGS. 5A-5Cshows peak intrinsic birefringence lobes with respect to the variouscrystal axis directions and the cubic crystalline lattice shown in FIG.4. The spatial orientation of the cubic crystalline lattice is indicatedby the other related crystalline lattice directions indicated by thearrows. For example, in FIG. 5A in which the center representsbirefringence encountered by a ray traveling along the [110] crystalaxis, a ray traveling along the [101] lattice direction is at a greaterangle with respect to the [110] crystal axis than a ray traveling alongthe [111] lattice direction; these ray angles are at 60° and 35.3°,respectively. This is indicated by the [101] arrowhead positioned at agreater radial distance from center than the [111] arrowhead. Therelative azimuthal directions of the indicated [100], [101], and [111]lattice directions are as shown in FIG. 4. This description applies toFIGS. 5B and 5C as well.

[0114] Referring to FIGS. 5A-5C, in each case, the indicated crystalaxis is the direction normal to the plane of the figure and at thecenter of each of the respective figures. FIG. 5A shows intrinsicbirefringence with respect to the [110] lattice direction, includingpeak intrinsic birefringence lobes 29A, 29B, 29C and 29D which eachforms an angle of 60° with respect to the [110] crystal axis direction.Intrinsic [110] birefringence also includes central birefringence node29E. FIG. 5B shows intrinsic birefringence with respect to the [100]lattice direction, including peak birefringence lobes 31A, 31B, 31C and31D each of which forms a 45° angle with respect to the [100] crystalaxis direction. There are also peaks along the diagonals at 90° notdepicted. FIG. 5C shows intrinsic birefringence along the [111] latticedirection and which includes peak birefringence lobes 33A, 33B, and 33C,each of which forms an angle of 35.3° with respect to the [111] crystallattice direction.

[0115] The crystal lattice and resulting intrinsic birefringence lobeswith respect to the crystal axes such as shown in FIGS. 5A-5C, are forthe exemplary embodiment in which the cubic crystals are negative cubiccrystals; that is the ordinary refractive index is greater than theextraordinary index, so the birefringence, n_(e)−n_(o), is negative.Calcium fluoride is an exemplary negative cubic crystal. For positivecubic crystals, the patterns would be substantially similar except thelines would be each rotated by 90 degrees about their midpoints. Itshould be understood that other cubic crystalline optical elements suchas barium fluoride, lithium fluoride, and strontium fluoride might beused as optical elements in other exemplary embodiments of the presentinvention. With respect to any cubic crystalline material used, thevariations in the intrinsic birefringence direction and magnitude can bemeasured, or calculated using computer modeling. Furthermore, thevariations in intrinsic birefringence direction and magnitude of anoptical material may also be measured. Graphical representations of thevariations in birefringence magnitude and axis orientations similar tothose shown in FIGS. 5A-5C, can be similarly generated for each of theaforementioned cubic crystalline materials.

[0116] Referring again to FIG. 1, it can be understood that if each ofindividual lens elements L is formed of the same cubic crystallineoptical material such as calcium fluoride and the individual lenselements L, or optical elements, are arranged along a common opticalaxis and aligned such that each of individual lens elements L that isconstructed from a cubic crystalline material, includes substantiallythe same three dimensional lattice orientation with respect to theoptical axis 10, then the net retardance of the lens system (i.e.,optical system 2) will have a retardance that varies across the systemexit pupil in a similar manner to the angular intrinsic birefringencevariation shown schematically in FIGS. 5A-5C.

[0117] Embodiment 1

[0118]FIG. 6 shows an exemplary arrangement of an optical system used todemonstrate the basic technique for mitigating the effects of intrinsicbirefringence. This exemplary optical system consists of an aberrationfree light beam converging toward a focus at a numerical aperture of0.707, giving maximum ray angles of 45° through each element. The beampasses through three cubic crystalline elements 42, 44 and 46 whoseradii of curvature are specified to be concentric with focal point 40 ofthe beam. Cubic crystalline elements 42, 44 and 46 have thicknesses 43,45 and 47, respectively. In an exemplary embodiment, each of thicknesses43, 45 and 47 may be 5 mm and cubic crystalline elements 42, 44 and 46may be assumed to have a birefringence magnitude, n_(e)−n_(o), of−12×10⁻⁷, corresponding to the intrinsic birefringence of calciumfluoride measured at a wavelength of 157 nm as suggested in D. Krahmer,“Intrinsic Birefringence in CaF₂,” at Calcium Fluoride BirefringenceWorkshop, Intl SEMATECH, Jul. 18, 2001, the contents of which are herebyincorporated by reference. In this exemplary configuration, the elementsdo not contribute wavefront aberration to the converging beam other thanretardance aberrations produced by intrinsic birefringence. For thisexample, the wavelength is 157.63 nm, and the ordinary index ofrefraction is assumed to be 1.5587.

[0119] In one exemplary embodiment, the optical system shown in FIG. 6may be arranged such that each of elements 42, 44 and 46 are arrangedalong a common optical axis and such that the three-dimensional crystallattice for each element is aligned identically. FIGS. 7A, 7B, and 7Cshow how the retardance varies over the exit pupil for cases in whichthe optical axis is along the [110], [100], and [111] latticedirections, respectively, and the three-dimensional crystal lattice foreach element is aligned identically.

[0120]FIGS. 7A, 7B and 7C are each graphical illustrations of netretardance magnitude and orientation across the pupil for the exemplaryoptical system shown in FIG. 6. In these plots, and the retardance pupilmaps to follow, the retardance is shown on a square grid across thesystem exit pupil for the optical system of interest, and is describedin general by ellipses which sometimes degenerate into lines that showthe eigenpolarization states (i.e., the polarization state that remainsunchanged for a ray propagating through the optical system at givenpupil coordinates). The size of the ellipse or length of the line at agiven pupil coordinate is proportional to the relative strength of theretardance and the angle is related to the angle of the retardance axis.

[0121] Also, for each of the lens and corresponding retardance mapembodiments described herein, the coordinates are defined using aright-handed coordinate system such that the system optical axis is inthe +Z direction from the object towards the image plane, the +Y axis isin the vertical direction, and the +X direction is orthogonal to the Yand Z axes. For all exit pupil retardance and wavefront maps providedherein, the plots describe variations over an exit pupil referencesphere for a given field point using a Cartesian coordinate system,where the X and Y coordinates are coordinates on the reference sphereprojected onto a plane perpendicular to the chief ray.

[0122] Returning now to FIGS. 7A, 7B, and 7C, it can be seen that, ineach case, the peak retardance is approximately 0.11 waves, and the RMSretardance is about 0.029 waves at a 157 nm wavelength. Thus, asignificant amount of retardance is produced for each of the opticalaxis directions through the crystal lattice in the exemplary commonlyaligned systems.

[0123] In the present invention, the crystal axes and relative rotationsof the individual elements with respect to the system optical axis areselected such that the retardance produced by the intrinsicbirefringence of the individual elements combines to minimize the netretardance experienced by light traveling through the system. The cubiccrystalline optical elements are oriented and clocked to produce a netretardance that is less than the sum of retardance produced by theintrinsic birefringence of the respective individual cubic crystallineoptical elements.

[0124] In one embodiment, the present invention provides at least threeoptical elements, in which at least two of the elements are orientedwith the optical axis along their [110] crystal axes and at least one ofthe elements is oriented with its [100] crystal axis along the systemoptical axis.

[0125] This embodiment may be applied to the exemplary optical systemshown in FIG. 6. In embodiment 1 of the present invention, the first twoelements 46 and 44 are oriented along the [110] cubic crystallinelattice direction and the third element 42 is oriented along the [100]lattice direction, although the specific order of the elements may bevaried in other exemplary embodiments. Furthermore, the crystal latticesof the [110] first 46 and second 44 elements are rotated by 90 degreeswith respect to one another in a plane perpendicular to the opticalaxis. This rotation about the optical axis is known as “clocking”.

[0126]FIGS. 8A, 8B, and 8C are graphical illustrations showing theretardance magnitude and orientation over the pupil for the individualelements in the arrangement of the first exemplary embodiment of theoptical system shown in FIG. 6, as described above. FIGS. 8A, 8B and 8Crepresent the individual retardance contributions for the first 46,second 44, and third 42 cubic crystalline optical elements,respectively. First element 46 is referred to as a [110] optical elementand is oriented with its [110] crystal axis along the system opticalaxis, such that the retardance along the optical axis is orientedhorizontally, as depicted in FIG. 8A. Second element 44 is referred toas a [110] optical element and is oriented with its [110] crystal axisalong the system optical axis, such that the retardance along theoptical axis is oriented vertically, as depicted in FIG. 8B. Thirdelement 42 is referred to as a [100] optical element and is orientedwith its [100] crystal axis along the optical axis, such that the peakbirefringence occurs along the pupil diagonals at azimuthal angles of±45 degrees, as depicted in FIG. 8C. Hereinafter, an optical elementreferred to as an [XYZ] optical element, is understood to be an opticalelement oriented with its [XYZ] lattice direction or its [XYZ] crystalaxis, along the system optical axis. By orienting the first two opticalelements with their [110] crystal axes along the optical axis, butrotated 90 degrees about the common system optical axis with respect toone another, the horizontally oriented retardance produced by firstelement 46 for light propagating near the optical axis may be balancedby the vertically-oriented retardance produced by second element 44.Because the retardance orientation of the second element is orthogonalto that of the first element and equal in magnitude, the effect is tocorrect the retardance aberration near the center of the pupil, andproduce a net retardance of essentially zero. Stated alternatively, thetwo individual retardances produced by first element 46 and secondelement 44, cancel each other to produce a net retardance of essentiallyzero. The first two optical elements therefore have theirthree-dimensional crystal lattices at a fixed rotation angle about theoptical axis with respect to each other. The elements are optimallyclocked such that respective birefringence lobes are aligned atdifferent three dimensional positions. Stated alternatively, the peakbirefringence lobes of the first two [110] optical elements 46 and 44are rotated with respect to each other. According to other exemplaryembodiments, the [110] optical elements may be rotated by angles otherthan 90 degrees and in still other exemplary embodiments, other cubiccrystalline optical elements may be used and rotated or clocked aboutthe optical axis and with respect to each other, such that theirrespective three dimensional lattice directions are not identicallyaligned and so as to produce a net retardance that is reduced relativeto the arrangement in which the elements have their three-dimensionalcrystal lattices aligned substantially identically.

[0127]FIG. 9A shows the net retardance of the first and second elementsof the first exemplary embodiment of the optical system depicted in FIG.6 and as described above. As shown, the retardance is corrected toessentially zero near the center of the pupil, as well as alonghorizontal and vertical sections bisecting the pupil. Residualretardance is noted, however, along the pupil diagonals, and is orientedat roughly ±45 degrees, directed towards the center of the pupil.

[0128] Returning to FIG. 8C, the retardance produced by third element 42of the first exemplary embodiment of the optical system depicted in FIG.6 oriented with its [100] crystal axis along the optical axis, has peakretardance along the diagonals of the pupil, but the magnitude of theretardance is opposite in sign to the net retardance produced by thefirst and second elements 46 and 44, as shown graphically in FIG. 9A. Inthe exemplary embodiment, the [100] optical element is rotated about thecommon optical axis such that the peak birefringence lobes are rotatedsubstantially by 45° with respect to the directions of the localbirefringence axes along the [110] crystal axes of the two, 90° clocked[110] optical elements. It can therefore be seen that the retardanceorientation for the contribution of the third element (FIG. 8C) isapproximately orthogonal to the net contribution from the first andsecond elements (FIG. 9A).

[0129]FIG. 9A shows that two [110] optical elements at 90 degreerelative rotations about the optical axis, produce a residual retardanceerror along the diagonals, but provide for corrected retardance alonghorizontal and vertical slices through the center of the pupil. Usingthe same principles, a [100] optical element may be used to furtherreduce the overall retardance.

[0130]FIG. 9B shows net retardance due to the contributions from allthree elements of the first exemplary embodiment of the optical systemdepicted in FIG. 6. It should be understood that the [100] opticalelement may be either first element 46, second element 44 or thirdelement 42, with essentially the same result. The residual netretardance is oriented roughly azimuthally and increases from zero atthe center of the pupil to a peak at the edge of the pupil. The peakretardance is approximately 0.019 waves, and the RMS retardance over thepupil is approximately 0.005 waves. In comparison to the uncorrectedbirefringence shown in FIGS. 7A, 7B and 7C, each having a peakretardance of approximately 0.11 waves and a RMS retardance ofapproximately 0.029 waves, it can be understood that the peak retardancehas been reduced by a factor of roughly six.

[0131] According to another exemplary embodiment in which thickness 43of third element 42 is about 2.3 mm, the peak retardance may be reducedto 0.0139 waves, with an RMS retardance of 0.0041 waves. This retardanceis shown in FIG. 9C. According to this exemplary embodiment, the peakretardance was reduced by a factor of approximately eight. According toother exemplary embodiments, other thicknesses may be used for elements42, 44 and 46 to yield different retardance values.

[0132] According to another exemplary embodiment, the residual error inFIG. 9B may be further reduced by a birefringent element that producesradially-oriented retardance that increases in magnitude from the centerto the edge of the component. Such an element may be produced byapplying a hoop stress to the edge of a meniscus optical component andadded to the exemplary optical system of the first embodiment and asshown in FIG. 6. The applied stress creates a spatially varyingbirefringence to compensate for the computed or measured birefringencevariation within the optical system as shown in FIG. 9B. Variousstresses may be applied to various optical elements to achieve thespatially varying birefringence. The stressed optical element may be alens element or a window and aligned along the optical axis. Varioustechniques may be used to apply the stress.

[0133]FIG. 9D shows the spatial radial retardance variation induced byapplying an exemplary compressive hoop stress of 1000 pounds per squareinch to first element 46 of FIG. 6. In this exemplary embodiment,element 46 has radii of curvature of 40 and 35 mm and a centralthickness of 5 mm. Differently shaped elements will have differentradial retardance variations, which can be used to substantially cancelthe retardance contributions such as those shown in FIG. 9B. The stressinduced birefringence varies spatially over the element, which isfundamentally different than retardance from intrinsic birefringencethat varies as a function of the angle of a ray with respect to thecrystal axis. This provides another important tool for reduction ofsystem retardance.

[0134] According to the exemplary embodiment illustrated in FIG. 6, inwhich the first two elements 46 and 44 are [110] cubic crystallineoptical elements, third element 42 is a [100] cubic crystalline opticalelement, and all elements are 5 mm thick, first element 46 may include atensile hoop stress of approximately 24 lbs./in² applied around theperimeter to minimize the net RMS retardance. The relative crystallattice orientations for optical elements 42, 44 and 46 are as describedabove.

[0135]FIG. 9E is a graphical representation depicting the individualretardance contribution due to the stress-induced birefringence of firstelement 46 shown in FIG. 6. FIG. 9E shows the individual contribution tothe retardance across the pupil for first element 46, when a tensilehoop stress of approximately 24 lbs./in² is applied around the perimeterof the element, and does not include the retardance caused by intrinsicbirefringence. FIG. 9E indicates a peak retardance of 0.0170 waves andRMS retardance of 0.0055 waves. In this exemplary embodiment, theradially oriented retardance produced by the stress element compensatesfor the residual retardance for the embodiment without stress-inducedbirefringence depicted in FIG. 9B.

[0136]FIG. 9F is a graphical illustration showing the net retardanceacross the pupil for the exemplary embodiment including thestress-induced birefringence of first element 46. With a tensile stressof approximately 24 lbs./in² applied to first element 46, the maximumresidual retardance is 0.0073 waves, and the RMS retardance is 0.0024waves for the optical system. This represents a significant improvementover the respective peak and RMS retardance values of 0.019 and 0.005waves, respectively, that result without applying stress-inducedbirefringence to first element 46, as shown in FIG. 9B. The appliedstress is intended to be exemplary only and various other appliedstresses of different magnitudes, may be used depending on the residualretardance of the system which, in turn, depends on the number and typesof cubic crystalline optical elements, the orientation and thickness ofthe optical elements, and the like.

[0137] According to yet another exemplary embodiment in which the firsttwo elements 46 and 44 are [110] cubic crystalline optical elements andthird element 42 is a non-cubic crystalline, non-birefringent element, atensile hoop stress may be applied around the perimeter of third element42 to minimize the net RMS retardance using the principles as above.Various stress values may be applied.

[0138] Another aspect of the present invention is the method formeasuring or using computer modeling to determine the retardance of anoptical system, identifying an optical element or elements to havestress-induced birefringence applied thereto, then applying thecompressive or tensile stress as a hoop or other stress, to producestress-induced birefringence as described above, to reduce residualretardance.

[0139] According to other exemplary embodiments having a residualretardance that is constant, or which varies after correction, variousbirefringent elements may be added to correct for the residualretardance. In an exemplary embodiment, a wave plate may be added to thesystem to correct for constant retardance; this wave plate mayconstructed from stressing a parallel plate. According to otherexemplary embodiments, a powered birefringent element having constantbirefringence magnitude may be used to compensate for residualvariations in retardance. The powered element may be a uniaxialcrystalline material or it may include a stress-induced birefringence,as above. Other optical elements with stress-induced birefringence mayadditionally or alternatively be used to correct for residual retardancevariation. The various exemplary optical elements may include a stressthat varies linearly across the element or quadratically in the radialdirection, along an axis substantially orthogonal to the optical axis.The birefringent element or elements will be chosen and positioned tocorrect for the constant or varying retardance residual in the systemafter correction as above.

[0140] Embodiment 2

[0141] According exemplary embodiment 2, the present invention providesan apparatus that achieves reduced retardance through the use of atleast four [110] optical elements and at least one [100] opticalelement. In the illustrated embodiment shown in FIG. 10, the presentinvention provides an apparatus having four elements with their [110]crystal axes along the system optical axis and one element with its[100] crystal axis along the system optical axis.

[0142] The relative orientations of the lattice directions in the planeperpendicular to the optical axis may be adjusted for the [110] opticalelements. This technique is known as “clocking” or rotating the crystallattice orientation of elements aligned along a common optical axis. Therelative orientations may be selected in a particular manner thatrelates to the azimuthal orientations of the off-axis peak birefringencelobes.

[0143] Referring to FIG. 4, there are peak birefringence lobes at 60°with respect to the [110] crystal axis, corresponding to the [011] and[101] directions (as well as two additional lobes not shown in FIG. 4).

[0144]FIG. 5A shows a retardance pupil map for a [110] optical element.As shown, the four outer birefringence lobes are not distributed byequal azimuthal angles. If the crystal lattice is defined to givehorizontally oriented retardance along the optical axis for a negativebirefringence magnitude, n_(e)−n_(o), the peaks are at azimuthal anglesof ±35.260 and ±144.74°.

[0145]FIG. 10 shows an optical system according to the second exemplaryembodiment. This exemplary five-element optical system consists of anaberration-free light beam converging toward a focus 50 at a numericalaperture of 0.707, giving maximum ray angles of 45° through eachelement. Cubic crystalline optical elements 52, 54, 56, 58 and 60 arealigned along optical axis 51. A light beam passes through five cubiccrystalline elements 52, 54, 56, 58 and 60 whose radii of curvature areeach concentric with the focal point 50 of the beam. In an exemplaryembodiment, the elements each have thicknesses of about 2.5 mm, and areassumed to have a birefringence magnitude each, n_(e)−n_(o), of−12×10⁻⁷, corresponding to the intrinsic birefringence of calciumfluoride measured at a wavelength of 157 nm. According to otherexemplary embodiments, other thicknesses may be used. In thisconfiguration, the elements do not contribute wavefront aberration tothe converging beam, other than retardance aberrations produced byintrinsic birefringence. According to an exemplary embodiment, thewavelength of light may be 157.63 nm, and the ordinary index ofrefraction may be 1.5587. Other wavelengths and indices of refractionmay be used in other exemplary embodiments.

[0146]FIGS. 11A, 11B, and 11C are graphical representations showing howthe retardance varies over the exit pupil for cases in which each ofelements 52, 54, 56, 58 and 60 of FIG. 10 are [110], [100], and [111]optical elements, respectively, and the three-dimensional lattice foreach element is aligned identically. In each case, the peak retardanceis approximately 0.095 waves, and the RMS retardance is about 0.024waves at the indicated wavelength of 157 nm. Thus, a significant amountof retardance is produced for each of the optical axis directionsthrough the crystal lattice.

[0147] According to the second exemplary embodiment, as applied to theexemplary optical system depicted in FIG. 10, the first four elements52, 54, 56 and 58 are oriented with their [110] crystal axes alongoptical axis 51 and fifth element 60 is oriented with its [100] crystalaxes along optical axis 51. According to other exemplary embodiments,the specific order of the components may be changed. According to thissecond exemplary embodiment, the relative clockings of the four elements52, 54, 56 and 58 with optical axes along the [110] direction, may be,in order, 17.632°, −17.632°, 72.368°, and −72.368°. Fifth [100] element60 is oriented such that the peak birefringence lobes are at azimuthalangles of ±45°.

[0148]FIGS. 12A to 12D show the retardance maps for the individualelement contributions for the four [110] optical elements in which thefour elements are clocked as described above.

[0149] Relative to an element clocking that provides horizontallyoriented retardance along the optical axis, first element 52 is rotatedby 17.632°, which locates the peak birefringence lobes at azimuthalangles of 52.897°, 162.368°, −17.632°, and −127.104°. The retardance mapfor the retardance contribution from first element 52 is shown in FIG.12A.

[0150]FIG. 12B shows the retardance contribution of second element 54,which is rotated by −17.632° to position the peak birefringence lobes atazimuthal angles of 17.632°, 127.104°, −52.897°, and −162.368°.

[0151]FIG. 12C shows the retardance contribution of third element 56,which is rotated by −72.368° to position the peak birefringence lobes atazimuthal angles of 107.632°, 37.104°, −72.368°, and −142.896°.

[0152]FIG. 12D shows the retardance contribution of fourth element 58,which is rotated by −72.368° to position the peak birefringence lobes atazimuthal angles of 72.368°, 142.896, −37.104°, and −107.632°. Therelative clockings of the four elements with optical axes along the[110] lattice direction are related to half of the azimuthal angle shownin FIG. 5A, i.e. ±17.632° or ±(90-17.632)°.

[0153] As shown in FIGS. 12A and 12D, the retardance contribution offirst element 52 is orthogonal to that of fourth element 58 near thecenter 61 of the pupil. Similarly, FIGS. 12B and 12C show that theretardance contribution of second element 54 is orthogonal to that ofthird element 56 near the center 61 of the pupil.

[0154]FIG. 13A shows the individual retardance contributions of thefirst and third elements 52 and 56 overlapping one another. Over centralportion 62 of the pupil, the retardance orientations are crossed at anaverage angle of roughly 45°. At positions 64 along the outer edge ofthe pupil and along the −45° diagonal, the retardance orientations arethe same.

[0155]FIG. 13B shows the net retardance for the combination of firstelement 52 and third element 56. Over a wide region of the pupil alongthe 45° diagonal, the retardance is oriented at a 45° angle. At the edgeof the pupil along the −45° diagonal, the retardance is oriented at−45°. Similarly, FIG. 13C shows the net retardance of second element 54and fourth element 58, which gives a retardance orientation over thepupil that is roughly orthogonal to the net retardance of the first andthird elements as shown in FIG. 13B.

[0156]FIG. 14A shows the net retardance for the four elements 52, 54, 56and 58 with their respective [110] crystal axes along optical axis 51,and oriented as described above. The maximum retardance is 0.0181 wavesand the RMS retardance is 0.0049 waves, which is a reduction inretardance of roughly a factor of five compared with all of the elementcrystal lattices aligned identically in three dimensions as depicted inFIGS. 11A, 11B and 11C. The residual retardance orientation is radialwith larger retardance magnitude along the ±45° diagonals.

[0157] The retardance contribution for fifth element 60, which isoriented to have its [100] lattice direction along the optical axis, isshown in FIG. 14B. As shown, the retardance is similar in magnitude tothe residual net retardance of the first four elements 52, 54, 56 and 58shown in FIG. 14A, and the orientation is generally perpendicular acrossthe pupil. This allows for nearly perfect correction or canceling of theretardance. According to the second exemplary embodiment in which thefirst four [110] optical elements 52, 54, 56 and 58 are aligned alongoptical axis 51 and have a net retardance shown in FIG. 14A and in whichthe fifth optical element 60 is aligned to have its [100] crystal axisalong optical axis 51, the net retardance for all five elements has amaximum of about 0.0007 waves and RMS retardance of 0.0002 waves asshown in FIG. 14C.

[0158] The second exemplary embodiment thus shows that four [110]optical elements and one [100] optical element with identicalthicknesses and ray angles are aligned to reduce the peak retardancefrom 0.0952 waves when all elements are identically oriented [110]elements, to a peak of 0.0007 waves, and the RMS retardance is reducedfrom 0.0229 waves to 0.0002 waves, a reduction by a factor of more than100 in both cases.

[0159] It should be understood that the first embodiment with two [110]optical elements and one [100] optical element, and the secondembodiment with four [110] optical elements and one [100] opticalelement, are exemplary only and that various numbers of optical elementsmay be used and clocked, in accordance with the preceding principles tobalance the individual intrinsic birefringence contributions of theelements and produce a reduced net birefringence and retardance. Theseprinciples may be applied to lens systems, including cubic crystallinelens elements exclusively or they may be applied to lens systemsincluding cubic crystalline and other lens elements.

[0160] Also as described in conjunction with embodiment 1, one or morestress birefringent elements, wave plates, or combinations thereof mayadditionally be used to correct for residual birefringence variation andconstant residual retardance which remains after the above-describedsystem corrections have been made.

[0161] Concepts of the Invention

[0162] The basic principles used to compensate the effects of intrinsicbirefringence, as applied to the first and second exemplary embodimentscorresponding to the exemplary lens arrangements shown in FIGS. 6 and10, respectively, can be extended to compensate for the effects ofintrinsic birefringence effects in various other high-performance, highnumerical aperture optical systems, such as those used forphotolithography in other exemplary embodiments. The principles applyboth to refractive and catadioptric lens systems and may be used whendesigning new lens systems or to improve a known lens prescription.

[0163] According to other exemplary refractive and catadioptric lenssystems, the individual lens element thicknesses, radii of curvature,aspheric coefficients, and ray angles may differ significantly fromcomponent to component. Additional non-cubic crystalline lens elementsmay optionally be included. Nonetheless, it will be shown in theembodiments to follow as in the previous embodiments, that the crystalorientation and relative clockings of the components may be chosen toreduce birefringence and therefore retardance. The illustratedembodiments show optical elements having their [110] crystal axes alongthe optical axis, used in conjunction with optical elements having their[100] crystal axes along the optical axis to balance, or cancelretardance aberrations produced by intrinsic birefringence. A generalconcept of the present invention is to provide an optical system whichincludes a projection lens formed of a plurality of optical elements,two or more of which are constructed from cubic crystalline material andoriented with their [110] cubic crystalline lattice direction along thesystem optical axis and with relative rotations about the optical axisto give reduced retardance for light propagating at small anglesrelative to the system optical axis, and one or more elements orientedwith the optical axis substantially along the [100] cubic crystallinelattice direction to give reduced retardance for light propagating atlarger angles with respect to the system optical axis, that is,locations off the optical axis.

[0164] In other embodiments, an element or elements having their [111]crystal axes aligned along the optical axis, as shown in FIG. 5C, may beused in conjunction with other element combinations to substantiallycancel the retardance throughout the field using the same principlesdescribed for the [110] and [100] embodiments. In various exemplaryembodiments, lens design software may be used to generate the lensprescription including positioning of the individual lens elements, aswell as thicknesses, radii of curvature, aspheric coefficients and thelike. In one embodiment, the RMS retardance may be computed over a pupilgrid at each field point and used as the merit function for a dampedleast squares optimization using the commercially available lenssoftware, CODE V, for example. A computer may be used to optimize theorientation and clocking of each of the elements in the system.

[0165] Phase aberrations, such as astigmatism, introduced by the averageindex variations in the cubic crystalline elements, may be compensatedusing one or more surfaces with different radii of curvature alongorthogonal directions. The variation in average index of refractionproduced by [100] optical elements is generally more easily compensatedthan the variation produced by [110] optical elements, due to a moregradual variation in average index of refraction as a function ofpropagation angle with respect to the optical axis. Therefore, asufficiently high number of [100] optical lens elements mayadvantageously be used along the optical axis to minimize high-ordervariations in average index of refraction.

[0166] According to other exemplary embodiments, the thicknesses of thecomponents, the spacings between the components, and the radii ofcurvature and aspheric coefficients of the lens elements, may similarlybe optimized to balance aberrations and reduce retardance across thefield. According to yet another exemplary embodiment, the cubiccrystalline lens elements may be selected and positioned such thatelements having a birefringence magnitude that is opposite in sign toanother lens element or elements, may be used together to substantiallycancel retardance produced by intrinsic birefringence and produce a netretardance of near zero throughout the field. For example, a calciumfluoride lens element (having a negative birefringence magnitude) may beused in conjunction with a barium fluoride lens element (having apositive birefringence magnitude) and aligned along the same crystallattice direction, so that the retardance throughout the field issubstantially cancelled.

[0167] The third, fourth and fifth embodiments are based on lensprescriptions published in the art. Such are intended to be exemplaryonly and the principles and concepts of the present invention may beapplied to any of various other lens arrangements. Application of thepresent invention is of particular interest for high numerical apertureoptical systems for photolithography at an exposure wavelength near 157nm, such as that produced by an F₂ excimer laser. Because many of theavailable optical systems described in the art include lower numericalapertures and operate at longer wavelengths such as 193 nm, thetechniques of the present invention are illustrated by application toexemplary known optical systems designed for an exposure wavelength near193 nm, corresponding to the wavelength produced by an ArF excimerlaser, commonly used in photolithography. It should be understood,however, that the principles and techniques of the present inventionapply equally to high numerical aperture systems and systems operatingat 157 nm.

[0168] To estimate the effects of intrinsic birefringence in highnumerical aperture lenses designed for a central wavelength of 157 nm,in which the refractive elements are primarily constructed from calciumfluoride, each element in the following embodiments, which may beconstructed from fused silica or calcium fluoride in the variousembodiments, is assumed to have a peak intrinsic birefringence of(n_(e)−n_(o))=−12×10⁻⁷, which is roughly equivalent to the measured peakintrinsic birefringence in calcium fluoride at a wavelength of 157 nm.

[0169] In this manner, the method for compensation of intrinsicbirefringence in similar high numerical aperture lenses designed for 157nm may be demonstrated using known exemplary lens descriptions designedfor a central wavelength of 193 nm as starting points. The change incentral wavelength may result in a change in refractive index of therefractive components and may warrant the use of fluoride materials suchas calcium fluoride, but the types of elements used and distributions ofray angles for a given numerical aperture are similar enough to allow alens designed for a central wavelength of 193 nm to be used todemonstrate the inventive techniques for mitigating the effects ofintrinsic birefringence in high numerical aperture lenses, particularlyat a central wavelength of 157 nm.

[0170] In the descriptions of embodiments 3, 4 and 5 that follow, eachrefractive surface is assumed to have a hypothetical, single layeranti-reflection coating with an index of refraction equal to the squareroot of the element index of refraction and with an optical thickness ofa quarter wave at a wavelength of 193.3 nm. The indices of refractionfor calcium fluoride and fused silica used in each of the embodimentsare assumed to be 1.501455 and 1.560326, respectively, at a wavelengthof 193.3 nm. Different coatings will introduce different retardance andphase aberrations and will require slightly different compensation. Itshould be understood, however, that the method demonstrated for thesingle hypothetical coating is applicable to systems with various otherphysical coatings.

[0171] In each of embodiments 3-5 that follow, the corrected opticalsystem is based on a given lens prescription. The given lensprescription may be maintained and the effects of intrinsicbirefringence compensated for, using the techniques described above, andadditionally or alternatively by the splitting of one or more lenselements of the given prescription, into two or more sub-elements. Theprinciples of the present invention may, however, be advantageously beapplied to various other new lens prescriptions being designed, with theadvantages of the present invention incorporated into the lens design.

[0172] Furthermore, one or more birefringent elements, wave plates, orcombinations thereof as described in conjunction with embodiments 1 and2, may additionally be used to correct for residual birefringencevariation and constant residual retardance after the describedcorrections have been made to the systems as described in embodiments 3,4 and 5.

[0173] Embodiment 3

[0174] The third exemplary embodiment for application of thecompensation techniques for intrinsic birefringence may be described inconjunction with an exemplary all-refractive projection lens used forphotolithography. Such an exemplary lens is provided in the fifthembodiment of European Patent No. 1 139 138 by Y. Omura, the contents ofwhich are herein incorporated by reference. This exemplary lens isdepicted in the schematic illustration of FIG. 15. This exemplary systemis designed to operate at a central wavelength of 193.3 nanometers,provides 4×reduction at a numerical aperture of 0.75, and has an imagefield diameter of 27.5 mm. The exemplary design employs 20 elements Ewith six aspheric surfaces constructed from calcium fluoride and fusedsilica; however, each component is assumed to have an intrinsicbirefringence of −12×10⁻⁷ in the following baseline computations. Theexemplary system includes optical axis 65.

[0175] The RMS and maximum retardance and diattenuation over the exitpupil are listed in Table 1 below for the nominal design withoutintrinsic birefringence effects included for relative field heights of0, 0.7, and 1.0. The relative field height is defined to be the actualfield height normalized by the semi-field height. Thus, an image locatedon the optical axis has zero field height and an image located at 13.75mm in this lens corresponds to unit relative field height. Theretardance and diattenuation result from the single-layeranti-reflection coatings used in the model. FIGS. 16A and 16B depict theretardance across the system exit pupil due to the anti-reflectioncoatings for the field points at the center and edge of the field,respectively. The retardance is radially-oriented and is largest inmagnitude at the edge of the pupil. The retardance due only to theanti-reflective coating is relatively small. TABLE 1 Retardance RelativeField (waves at λ_(o) = 193.3 nm) Diattenuation Height RMS Maximum RMSMaximum 0.0 0.0033 0.0125 0.0053 0.0217 0.7 0.0034 0.0132 0.0053 0.02301.0 0.0035 0.0149 0.0057 0.0247

[0176]FIGS. 17A and 17B show the diattenuation variation across thepupil for the center and edge of the field, respectively, for theoptical system illustrated in FIG. 15. Diattenuation may be described asa measure of the maximum difference in transmission between orthogonalpolarization states.

[0177] The RMS and peak-to-valley wavefront error are listed in Table 2below for the nominal design, without the effects of intrinsicbirefringence. The wavefront errors are given for relative field heightsof 0, 0.7, and 1.0 in the Y direction, and are listed for two orthogonalpolarization components. The X component represents the wavefront errorfor an input polarization in the X direction assuming a linear polarizeralong the X direction at the system exit pupil. The Y componentrepresents the wavefront error for an input polarization in the Ydirection assuming a linear polarizer along the Y direction at the exitpupil. As shown, the nominal design includes a peak RMS wavefront errorof about 0.003 waves. TABLE 2 Peak-to-Valley RMS Wavefront ErrorWavefront Error (waves at λ_(o) = 193.3 nm) (waves at λ_(o) = 193.3 nm)Relative Field X Y X Y Height Component Component Component Component0.0 0.002 0.002 0.012 0.012 0.7 0.003 0.002 0.020 0.020 1.0 0.003 0.0020.018 0.012

[0178] In FIGS. 18A, 18B, 18C, and 18D, wavefront errors at a wavelengthof 193.3 nm are plotted at the system exit pupil as contour maps. FIGS.18A and 18B show contour plots of the residual wavefront error for thelens depicted in FIG. 15 corresponding to an input polarization in the Xdirection (perpendicular to the field height) used with an exit pupilanalyzer in the X direction for the central and extreme field points,respectively. For the wavefront error at the central field point shownin FIG. 18A, the maximum peak-to-valley optical path difference is 0.012waves, and for the wavefront error at the extreme field shown in FIG.18B, the maximum peak-to-valley optical path difference is approximately0.018 waves. FIGS. 18C and 18D show contour plots of the residualwavefront error for the lens depicted in FIG. 15 corresponding to aninput polarization in the Y direction (parallel to the field height)used with an exit pupil analyzer in the Y direction for the central andextreme field points, respectively. For the wavefront error at each ofthe central and extreme field points shown in FIGS. 18C and 18D,respectively, the maximum peak-to-valley optical path difference isapproximately 0.012 waves.

[0179] The centroid distortion for the nominal design, calculated basedon the point spread function, and the telecentricity error in the Ydirection are listed in Table 3 below at relative field heights of 0,0.7, and 1.0. TABLE 3 Relative Field X PSF Centroid Y PSF Centroid YTelecentricity Height Distortion (nm) Distortion (nm) Error (mrad) 0.00.00 0.00 0.00 0.7 0.00 4.05 0.28 1.0 0.00 3.45 1.28

[0180] When the effects of intrinsic birefringence associated with thecubic crystalline lens material are taken into account, systemperformance degrades significantly. FIGS. 19A and 19B are graphicalillustrations showing the net retardance across the system exit pupilfor field points at the center and edge of the field, respectively,according to the arbitrarily designated exemplary embodiment in whichall lens elements E, shown in FIG. 15, are identically aligned in threedimensions, with the elements having their [110] crystal axis alongoptical axis 65. FIGS. 19A and 19B include the effects of intrinsicbirefringence. The object field height in FIG. 19A is 0 mm and theobject field height in FIG. 19B is 55 mm, corresponding to the centerand edge field points, respectively. In the retardance pupil maps givenin FIGS. 19A and 19B, and in others to follow in which the netretardance exceeds a magnitude of 0.5 waves, the retardance is plotted“modulo 0.5 waves.” It can therefore be seen that the retardanceorientation rotates by 90 degrees at one-half-wave intervals, i.e., theeffect of a 0.75 wave retarder at 0 degrees is the same as a 0.25 waveretarder at 90 degrees. Thus, the peak retardance due to intrinsicbirefringence in this exemplary arrangement is approximately 1.5 wavesat a wavelength of 193.3 nanometers, with small variation with objectfield height.

[0181]FIGS. 20A and 20B are graphical illustrations of the retardance ofanother exemplary embodiment of crystal lattice orientation of the lenssystem shown in FIG. 15. In FIGS. 20A and 20B, the net retardance acrossthe system exit pupil, including the effects of intrinsic birefringence,is depicted for field points at the center and edge of the field withall elements arbitrarily aligned identically in three dimensions, withtheir [100] crystal axes along the optical axis. Again, the retardanceorientation rotates by 90 degrees at one-half-wave intervals; thus, thepeak retardance due to intrinsic birefringence in this example isapproximately 0.9 waves at a wavelength of 193.3 nanometers.

[0182]FIGS. 21A and 21B are graphical illustrations of the retardance ofanother exemplary embodiment of crystal lattice orientation of the lenssystem shown in FIG. 15. In FIGS. 21A and 21B, the net retardance acrossthe system exit pupil is depicted for field points at the center andedge of the field with all elements arbitrarily aligned identically inthree dimensions, for [111] optical elements. In this exemplaryarrangement, the peak retardance due to intrinsic birefringence isapproximately 0.5 waves at a wavelength of 193.3 nanometers, and thevariation with field height is small.

[0183] Each of three preceding examples, as illustrated in FIGS.19A-21C, shows that the intrinsic birefringence produces very largeretardance aberrations and consequently large wavefront aberrations,when each of the elements are oriented identically with respect to theoptical axis. Without compensation, this aberration strongly exceeds theallowable wavefront error for photolithography.

[0184] In the present embodiment of the present invention, the variablesused for compensation of the retardance produced by the intrinsicbirefringence described above are the orientations of the crystal axisfor each element with respect to the optical axis and the relativerotations of those elements about the optical axis. The rotation of alens element with rotationally symmetric surfaces about its optical axisis sometimes referred to as element ‘clocking.’

[0185] One aspect of the present invention is the use of at least two[110] optical elements and at least one [100] optical element alignedalong an optical axis. This allows the retardance contributions of theindividual elements to be balanced to provide wavefront correction andreduce the net retardance produced by the intrinsic birefringence to alevel that is acceptable for high numerical aperture lithographysystems. This was described in the first embodiment and is alsoapplicable to embodiment 3, as will be shown.

[0186]FIG. 22 shows the third embodiment of the present invention asapplied to the optical system previously shown in FIG. 15. FIG. 22 is aschematic, side view of the lens. In this embodiment, elements E1, E5,E6, E13, E14, E15, and E18, numbered with respect to the object plane70, are aligned with their [100] crystal axes along optical axis 75, andall other elements E are aligned with their [110] crystal axes alongoptical axis 75. In FIG. 22, each of the [100] optical elements (E1, E5,E6, E13, E14, E15 and E18) is hatched.

[0187] The directions of the crystal lattices and clockings of each ofthe components are given in Table 4 below for the third exemplaryembodiment. For [110] optical elements oriented with their [110] opticalaxis along optical axis 75, the clocking of each element is givenrelative to an orientation that produces peak birefringence along theoptical axis that is oriented with the retardance axis substantiallyparallel to the X axis (horizontal, in the direction perpendicular tothe specified field of view). For [100] optical elements oriented withtheir [100] crystal axis along optical axis 75, the clocking of eachelement is given relative to an orientation that produces peakbirefringence lobes in the X-Z and Y-Z planes (at radial angles of 0,90, 180, and 270 degrees). It should be understood that such isexemplary only and the relative clocking of the elements may bedescribed with respect to any of various arbitrary reference locations.TABLE 4 Crystal Axis along Optical Element Clocking Element Axis(degrees) E1 [100] 14.20 E2 [110] -45.84 E3 [110] 35.47 E4 [110] -52.88E5 [100] 28.30 E6 [100] 28.69 E7 [110] 72.03 E8 [110] -28.62 E9 [110]63.44 E10 [110] 5.06 E11 [110] 79.87 E12 [110] 5.73 E13 [100] 30.26 E13,— -52.00 Surface S2 E14 [100] 10.01 E15 [100] 15.09 E16 [110] -26.15 E17[110] -105.71 E18 [100] 1.69 E19 [110] 145.51 E20 [110] 35.55 Image —0.0000133

[0188] The net intrinsic birefringence of the system is significantlyreduced as a result of the element orientation as shown in Table 4.

[0189] Another effect produced by intrinsic birefringence in the cubiccrystal lattice is variation of the average index of refraction as afunction of ray angle through the cubic crystalline material. Aftercompensation of the retardance errors resulting from intrinsicbirefringence as above, the residual wavefront aberrations anddistortion resulting from the variations in average index of refractionmay desirably also be compensated. This variation in average index ofrefraction typically produces astigmatism in the wavefront and mayresult in distortion of the image that may be balanced in the opticaldesign. This distortion may include image shift, image rotation,magnification error, or higher order distortion.

[0190] In this third exemplary embodiment, further modifications made tothe optical design compensate for the effects of variations in averageindex of refraction. Surface S2 of element E13, the surface immediatelypreceding aperture stop 72, is non-rotationally symmetric or includes anasymmetric variation in curvature. In the exemplary embodiment, surfaceS2 of element E13 is a toroidal surface in which the radius of curvaturein orthogonal directions varies along with the clocking of the surface.

[0191] Table 5 shows that the radius of curvature for S2 in the local Xdirection differs from that in the local Y direction. The radii ofcurvature of the last seven surfaces are adjusted to balance residualdistortion, and the image plane rotated to remove residual imagerotation. The revised radii of curvature are listed in Table 5 below,and the image plane rotation is given in Table 4 above. Although thenon-rotationally symmetric element is a [100] optical element in theexemplary embodiment, the toroidal or other non-rotationally symmetricsurface may be used on other cubic crystalline or non-cubic crystallineoptical elements in other exemplary embodiments. In various exemplaryembodiments, an optical element may include a pair of surfaces that eachhave an asymmetric variation in curvature. TABLE 5 Surface Radius ofCurvature (mm) E13, Surface S2, local X direction -913.123746 E13,Surface S2, local Y direction -913.128860 E17, Surface S1 179.985780E17, Surface S2 309.315227 E18, Surface S1 150.015302 E18, Surface S2225.037081 E19, Surface S1 114.371026 E19, Surface S2 390.970966 E20,Surface S1 -7083.652132 E20, Surface S2 Infinite

[0192] An aspect of the present invention is that the retardancecompensation that may be achieved in a high-performance optical systemis relatively insensitive to changes in ray angles through thecomponents within the field of view. Referring to FIG. 4, the outer peakbirefringence lobes are each at a 60° angle with respect to the [110]crystal axis. This angle is particularly large compared with thecorresponding angles of 45° and 35.26° for the [100] and [111] crystalaxes, respectively, also shown in FIG. 4. Thus, selecting the [110]crystal axis for a substantial number of components allows retardancecorrection over a large field of view.

[0193]FIGS. 23A and 23B are graphical representations that depict theretardance across the system exit pupil for the compensated systemdetailed above and described in Tables 4 and 5. The retardance is causedby the intrinsic birefringence and anti-reflection coatings. Aspreviously shown in FIGS. 16A and 16B, the contribution due the coatingsis relatively small; thus, the bulk of the retardance aberration is dueto the intrinsic birefringence. FIG. 23A shows retardance at the centerfield point and FIG. 23B shows retardance at the edge field point.

[0194] The RMS and maximum retardance over the exit pupil are listed inTable 6 below for relative field heights of 0, 0.7, and 1.0. Theseinclude the effects of intrinsic birefringence and the single layeranti-reflection coatings used in the model. A relative field height of0.0 corresponds to the center field point shown graphically in FIG. 23A,and a relative field height of 1.0 corresponds to the edge field pointshown graphically in FIG. 23B. The RMS retardance ranges from 0.0086 to0.0105 waves at λ_(o)=193.3 nm. TABLE 6 Retardance (waves at λ_(o) =193.3 nm) Relative Field Height RMS Maximum 0.0 0.0086 0.0524 0.7 0.00930.0529 1.0 0.0105 0.0597

[0195] The RMS and peak-to-valley wavefront error for the exemplarycorrected system of the third embodiment are listed in Table 7 below forthe compensated design that includes the effects of intrinsicbirefringence. These data are shown graphically for relative fieldheights of 0.0 and 1.0 in FIGS. 23A and 23B, respectively. The wavefronterrors are given for relative field heights of 0, 0.7, and 1.0 in the Ydirection, and are listed for two orthogonal polarization components.The X component represents the wavefront error for an input polarizationin the X direction assuming a linear polarizer along the X direction atthe system exit pupil. The Y component represents the wavefront errorfor an input polarization in the Y direction assuming a linear polarizeralong the Y direction at the exit pupil. With the effects of intrinsicbirefringence included, an RMS wavefront error that varies from 0.008 to0.010 waves across the field has been achieved due to the correctiontechnique. The peak-to-valley wavefront error has been reduced by afactor of about 27, compared with alignment of all elements along the[110] lattice direction. Thus, this embodiment demonstrates thatintrinsic birefringence effects can be reduced to a level acceptable forhigh numerical aperture lithography. TABLE 7 Peak-to-Valley RMSWavefront Error Wavefront Error (waves at λ_(o) = 193.3 nm) (waves atλ_(o) = 193.3 nm) Relative Field X Y X Y Height Component ComponentComponent Component 0.0 0.009 0.010 0.057 0.041 0.7 0.008 0.009 0.0560.046 1.0 0.008 0.010 0.051 0.055

[0196]FIGS. 24A, 24B, 24C, and 24D show wavefront errors plotted at thesystem exit pupil as contour maps. FIGS. 24A and 24B show contour plotsof the residual wavefront error for the exemplary lens depicted in FIG.22 corresponding to an input polarization in the X direction(perpendicular to the field height) used with an exit pupil analyzer inthe X direction for the central and extreme field points, respectively.For the wavefront error at the central field point shown in FIG. 24A,the maximum peak-to-valley optical path difference is approximately0.057 waves at a wavelength of 193.3 nanometers, and for wavefront errorat the at the extreme field shown in FIG. 24B, the maximumpeak-to-valley optical path difference is approximately 0.051 waves.FIGS. 24C and 24D show contour plots of the residual wavefront error forthe lens depicted in FIG. 22 corresponding to an input polarization inthe Y direction (parallel to the field height) used with an exit pupilanalyzer in the Y direction for the central and extreme field points,respectively. For the wavefront error at the central field point shownin FIG. 24C, the maximum peak-to-valley optical path difference isapproximately 0.041 waves at a wavelength of 193.3 nanometers, and forthe wavefront error at the extreme field shown in FIG. 24D, the maximumpeak-to-valley optical path difference is approximately 0.055 waves.

[0197] The centroid distortion for the compensated design with intrinsicbirefringence, calculated based on the point spread function, and thetelecentricity error in the Y direction are listed at relative fieldheights of 0, 0.7, and 1.0 in Table 8 below. Telecentricity errors aredeviations from normal incidence of the cone of rays at the image plane.As shown, the residual distortion in the X and Y directions is wellwithin 0.1 nm, which is suitable for 157 nm lithography. The distortionhas also been significantly reduced relative to distortion for thenominal design described in Table 3. Changes in telecentricity errorfrom the nominal design are negligible. TABLE 8 Relative Field X PSFCentroid Y PSF Centroid Y Telecentricity Height Distortion (nm)Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.00 0.7 -0.06 -0.05 0.28 1.00.08 -0.05 1.28

[0198] Table 9 provides a summary of the performance of the design interms of the Strehl ratio. The Strehl ratio describes the peak intensityof the point spread function relative to that of an aberration-freesystem. The effects of polarization and apodization are included in thiscalculation, as well as wavefront aberrations. At high numericalaperture, an aberration free optical system does not have a perfectStrehl ratio, a value of unity, due to variations in polarizationresulting from interference of rays at large angles with respect to oneanother. In the present example, the Strehl ratio values are calculatedat field points centered on the point-spread function, i.e., distortioneffects were not considered.

[0199] Table 9 shows an aberration free system at 0.75 NA having aStrehl ratio of 0.8434. The performance of the nominal design withoutintrinsic birefringence effects is very similar to that of an idealaberration free lens; the Strehl ratio differs over a range of −0.0004to +0.0005 It is understood that the Strehl ratio may exceed that of aperfect lens due to differences between physical and ideal lens models.

[0200] For the compensated system with intrinsic birefringence, theStrehl ratio is similar to that of the nominal design withoutconsidering the effects of intrinsic birefringence, and also similar tothe ideal 0.75 NA aberration free system. TABLE 9 Strehl Ratio DesignLayout On-Axis Field 70% Field Extreme Field Aberration-free lens 0.84340.8434 0.8434 (0.75 NA) Nominal, no birefringence 0.8436 0.8439 0.8430considered Elements aligned to 0.8389 0.8377 0.8361 compensate

[0201] In summary, this third exemplary embodiment describes a lens withseven [100] optical elements and thirteen [110] optical elements. Therelative clockings of the elements are given in Table 4. When used in aspace in which the ray angles through the crystal are small with respectthe optical axis, the retardance introduced by the component is smallwhen the optical axis is along the [100] crystal axis of the material.Thus, such elements are generally insensitive to clocking, and it ispossible to use the clocking of these components to compensate formanufacturing errors during fabrication, such as non-rotationallysymmetrical defects. For example, the first six [100] optical elementsmay be varied in clocking without significant loss of performance,according to other exemplary embodiments. In another exemplaryembodiment, the plurality of [100] optical elements may therefore beused to compensate for residual aberrations due to non-rotationallysymmetric figure errors on the lens elements more easily than in a lenswith more [110] and fewer [100] cubic crystalline elements.

[0202] Embodiment 4

[0203] The fourth exemplary embodiment for application of thecompensation techniques for intrinsic birefringence may be described inconjunction with another exemplary all-refractive projection lens. Suchan exemplary lens may be used for photolithography and, in particular,may be used in the semiconductor manufacturing industry. Such anexemplary lens is provided in the seventh embodiment disclosed inEuropean Patent No. 1 139 138 A1 to Y. Omura. This exemplary lens isdepicted in FIG. 1. It is designed to operate at a central wavelength of193.3 nanometers, provides 4×reduction at a numerical aperture of 0.75,and has an image field diameter of 27.5 mm. The design employstwenty-eight optical elements with three aspheric surfaces constructedfrom calcium fluoride and fused silica; however, each component isassumed to have an intrinsic birefringence of −12×10⁻⁷ in the followingcalculations used to illustrate the principles of the present invention.According to other exemplary embodiments, some of the lens elements maybe formed of non-cubic crystalline material or additional lens elementsformed of non-cubic crystalline material may be used. Various suitablenon-cubic crystalline materials such as dry fused silica may be used.

[0204] RMS and maximum retardance and diattenuation over the exit pupilare listed in Table 10 for the nominal design without intrinsicbirefringence effects included for relative field heights of 0, 0.7, and1.0. The retardance and diattenuation result from the single-layeranti-reflection coatings used in the model. TABLE 10 RMS Maximum RMSMaximum 0.0 0.0048 0.0177 0.0068 0.0273 0.7 0.0052 0.0202 0.0074 0.02961.0 0.0055 0.0239 0.0080 0.0358

[0205]FIGS. 25A and 25B are graphical representations showing theretardance across the system exit pupil due to the anti-reflectioncoatings for the field points at the center and edge of the field,respectively. The retardance is radially-oriented and is largest inmagnitude at the edge of the pupil. FIGS. 26A and 26B are graphicalrepresentations showing diattenuation variation across the pupil for thecenter and edge of the field, respectively.

[0206] Table 11 shows RMS and peak-to-valley wavefront error for thenominal design, without the effects of intrinsic birefringence.Wavefront errors are given for relative field heights of 0, 0.7, and 1.0in the Y direction, and are listed for two orthogonal polarizationcomponents. The X component represents the wavefront error for an inputpolarization in the X direction assuming a linear polarizer along the Xdirection at the system exit pupil. The Y component represents thewavefront error for an input polarization in the Y direction assuming alinear polarizer along the Y direction at the exit pupil. Without cubiccrystalline optical elements, or the effect of intrinsic birefringenceconsidered, the nominal design includes a peak RMS wavefront error of0.004 waves. TABLE 11 RMS Wavefront Error Peak-to-Valley Wavefront ErrorRelative Field (waves at λ_(o) =193.3 nm) (waves at λ_(o) = 193.3 nm)Height X Component Y Component X Component Y Component 0.0 0.003 0.0030.017 0.017 0.7 0.003 0.004 0.022 0.033 1.0 0.003 0.004 0.022 0.029

[0207]FIGS. 27A, 27B, 27C, and 27D show wavefront errors plotted at thesystem exit pupil as contour maps for the nominal design withoutintrinsic birefringence effects included. FIGS. 27A and 27B show contourplots of the residual wavefront error for the exemplary lens depicted inFIG. 1 corresponding to an input polarization in the X direction,perpendicular to the field height, used with an exit pupil analyzer inthe X direction for the center and extreme field points, respectively.For the wavefront error at the central field point, the maximumpeak-to-valley optical path difference is 0.017 waves at a wavelength of193.3 nanometers, and for the wavefront error at the extreme field, themaximum peak-to-valley optical path difference is 0.022 waves. FIGS. 27Cand 27D show contour plots of the residual wavefront error for the lensdepicted in FIG. 1 corresponding to an input polarization in the Ydirection, parallel to the field height, used with an exit pupilanalyzer in the Y direction for the central and extreme field points,respectively. For the wavefront error at the central field point, themaximum peak-to-valley optical path difference is 0.017 waves at awavelength of 193.3 nanometers, and for the wavefront error at theextreme field, the maximum peak-to-valley optical path difference is0.029 waves.

[0208] Table 12 shows the centroid distortion for the nominal design,calculated based on the point spread function, and the telecentricityerror in the Y direction at relative field heights of 0, 0.7, and 1.0.TABLE 12 Relative Field X PSF Centroid Y PSF Centroid Y TelecentricityHeight Distortion (nm) Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.000.7 0.00 7.70 0.11 1.0 0.00 10.70 0.51

[0209] In an actual lens design using the lens prescription shownschematically in FIG. 1 and including cubic crystalline opticalelements, intrinsic birefringence is included. With the effects ofintrinsic birefringence included, performance degrades significantly.FIGS. 28A and 28B show the net retardance across the system exit pupilfor field points at the center and edge of the field (at object fieldheights of 0 and 55 mm) according to an exemplary embodiment in whichall elements are identically aligned in three dimensions, with element[110] crystal axes along optical axis 10. In these plots, the retardanceorientation rotates by 90 degrees at one-half-wave intervals, i.e., theeffect of a 0.75 wave retarder at 0 degrees is the same as a 0.25 waveretarder at 90 degrees. Thus, the peak retardance due to intrinsicbirefringence in this example is approximately 2.1 waves at a wavelengthof 193.3 nanometers.

[0210]FIGS. 29A and 29B show the net retardance across the system exitpupil for field points at the center and edge of the field,respectively, according to another exemplary arrangement in which allelements are identically aligned in three dimensions, with element [100]crystal axes along optical axis 10. Again, the retardance orientationrotates by 90 degrees at one-half-wave intervals; thus, the peakretardance due to intrinsic birefringence in this example isapproximately 1.5 waves at a wavelength of 193.3 nanometers.

[0211]FIGS. 30A and 30B show the net retardance across the system exitpupil for field points at the center and edge of the field,respectively, according to another exemplary arrangement in which allelements are aligned identically in three dimensions, with element [111]crystal axes along optical axis 10. In this exemplary arrangement, thepeak retardance due to intrinsic birefringence is approximately 0.8waves at a wavelength of 193.3 nanometers.

[0212] With all elements aligned with their [110], [100], or [111]crystal axes along optical axis 10, and oriented identically in threedimensions, the retardance produced by intrinsic birefringence producesvery large wavefront aberration. Without compensation, this aberrationstrongly exceeds the desirable wavefront error required forphotolithography processes, particularly for photolithography processesused to produce the small feature sizes in today's semiconductormanufacturing industry.

[0213] The fourth exemplary embodiment achieves compensation of theretardance produced by intrinsic birefringence by prescribing theorientations of the cubic crystal lattice for each element with respectto its optical axis, and the relative rotations of those elements aboutthe optical axis to correct for intrinsic birefringence of the system.Furthermore in the fourth embodiment, as illustrated in FIG. 31, two ofthe elements of the exemplary lens system of FIG. 1 have each been splitinto two segments that have the same total thickness and power, with thethicknesses for the two segments and the curvature of the buried surfacebetween them optimized to minimize the net system retardance. Theseadditional degrees of freedom are shown to improve the achievableretardance compensation without requiring redesign of the lens.

[0214] According to the fourth embodiment, a combination of [110]optical elements and [100] optical elements is used to allow theretardance contributions of the individual elements to substantiallycancel each other and provide an overall wavefront correction that isacceptable for high numerical aperture lithography systems.

[0215]FIG. 31 is a schematic side view of the improved lens. Lens 100includes object plane 80, which may be a reticle or photomask, imageplane 82, which may be a substrate upon which the image is formed,optical axis 85, and aperture stop, AS, 89. The [100] optical elements,L28A and L28B, are hatched. In this embodiment, all other elementsL1-L27B are [110] optical elements aligned with their [110] crystal axesalong optical axis 85.

[0216] The fourth embodiment provides a lens 100 shown in FIG. 31 thatincludes lens elements L1-L28B having crystal axes and clockings givenin Table 13. For [110] optical elements, the clocking of each element isgiven relative to an orientation that produces peak birefringence alongthe optical axis that is oriented with the retardance axis substantiallyparallel to the X axis (horizontal, in the direction perpendicular tothe specified field of view). For [100] optical elements, the clockingof each element is given relative to an orientation that produces peakbirefringence lobes in the X-Z and Y-Z planes—at radial angles of 0, 90,180, and 270 degrees. TABLE 13 Crystal Axis along Optical ElementClocking Element Axis (degrees) L1  [110] 51.93 L2  [110] −82.04 L3 [110] −33.00 L4  [110] 71.15 L5  [110] −35.37 L6  [110] 27.46 L7  [110]21.75 L8  [110] −70.79 L9  [110] −43.04 L10 [110] −39.84 L11 [110] 35.04L12 [110] −63.29 L13 [110] 58.42 L14 [110] −3.10 L15 [110] 67.64 L16[110] 58.53 L17 [110] 49.69 L18 [110] 68.53 L19 [110] 29.79 L20 [110]−75.69 L20, Surface 2 Zernike Surface −75.69 L21 [110] −25.98 L22 [110]54.09 L23 [110] 42.29 L24 [110] 54.60 L25 [110] −21.99 L26 [110] 15.35 L27A [110] −57.40  L27B [110] 68.88  L28A [100] 40.25  L28B [100] 82.87Image — −0.00000199

[0217] The fourth exemplary embodiment illustrates another aspect of thepresent invention, namely, reducing intrinsic birefringence andretardance of a known lens system. This aspect of the present inventionincludes providing a given lens prescription having good opticalqualities and including multiple individual lens elements. For thisgiven lens prescription, at least one of the individual lens elements isreplaced by, or split into, two or more sub-elements. The sub-elementseach include the same overall radius of curvature and include the samethickness so that the overall optical qualities of the lens prescriptionare not adversely affected. For each individual element being replaced,the sub-elements are oriented to reduce net system retardance relativeto the retardance correction achievable using the individual lenselement which they combine to replace.

[0218] In one exemplary embodiment, each of the sub-elements may bealigned with the same crystal axis along the optical axis, and thesub-elements may be clocked relative to each other. For example, each ofthe sub-elements may be a [110] or [100] optical element. In anotherexemplary embodiment, the elements may include different crystal axesaligned along the optical axis, for example, a [100] optical element anda [110] optical element. This concept is illustrated by comparing lens 2in FIG. 1 to lens 100 shown in FIG. 31. Lens 2 shown in FIG. 1 includesmultiple lens elements, including lens elements L101 and L102. Lens 100in FIG. 31 is substantially similar to lens 2 of FIG. 1, with theexception being that lens element L101 of FIG. 1 is replaced by twosub-elements-lens sub-elements L27A and L27B of FIG. 31, and lenselement L102 of lens 2 in FIG. 1 is replaced by two lens sub-elements,namely, lens sub-elements L28A and L28B shown in FIG. 31.

[0219] Another effect produced by intrinsic birefringence in the cubiccrystal lattice is variation of the average index of refraction as afunction of ray angle through the crystal. In addition to compensatingfor retardance errors resulting from intrinsic birefringence, thepresent invention provides for correcting for residual wavefrontaberrations and distortion resulting from the variations in averageindex of refraction. If uncorrected, this variation in average index ofrefraction may produce astigmatism in the wavefront and may result indistortion of the image. This distortion may include image shift, imagerotation, magnification error, or higher order distortion.

[0220] As such, in the fourth embodiment, the optical design includesmodifications, relative to lens 2 of FIG. 1, to compensate for theeffects of variations in average index of refraction. Surface S2 of lenselement L20, the right hand surface of the lens element immediatelyfollowing aperture stop 89, includes a shape defined by Zernikepolynomials as described below. The Zernike coefficients are adjusted tocompensate for residual astigmatism. The Zernike coefficients may beused to adjust the surface shape of other elements and one or multiplesurfaces with an asymmetric variation in curvature, may be utilized inother exemplary embodiments. Also, the radii of curvature of tensurfaces are adjusted to balance residual distortion, and image planerotation is provided to remove residual image rotation. The resultingradii of curvature and Zernike surface coefficients, C_(j,) are listedin Table 14, and the image plane rotation is given in Table 13.

[0221] The Zernike polynomials, Z_(j,) are defined with respect to acircle with the normalization radius listed. Surface sag, Z(x, y), theintegral of which describes the surface, is described by the followingequation:${Z\left( {x,y} \right)} = {\frac{c\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {c^{2}\left( {x^{2} + y^{2}} \right)}}} + {\sum\limits_{j = 1}^{4}\quad {C_{j}Z_{j}}}}$

[0222] where c is the curvature=1/(radius of curvature) and x and y arethe Cartesian coordinates on the surface. TABLE 14 Surface Radius ofCurvature (mm) L24, Surface S1 277.35519 L24, Surface S2 1289.10376 L25,Surface S1 179.54899 L25, Surface S2 446.44705 L26, Surface S1 182.12274L26, Surface S2 558.39223 L27A, Surface S1 −10831.04108 L27A, Surface S2154.82711 L27B, Surface S1 154.82711 L27B, Surface S2 322.35847 L28A,Surface S1 399.66226 L28A, Surface S2 −2608.81885 L28B, Surface S1−2608.81885 L28B, Surface S2 −1902.32780 Parameter Zernike Polynomial,Z_(j) Zernike Coefficient, C_(j) C₁ x² − y² −1.7603 × 10⁻⁶ C₂ 2xy−2.5077 × 10⁻⁵ C₃ [4(x² + y²) − 3](x² − y²)  1.0700 × 10⁻⁵ C₄ 2[4(x² +y²) − 3]xy  1.1000 × 10⁻⁶ Normalization Radius — 136.1 mm

[0223] In summary, in the fourth embodiment, two elements—lens elementsL101 and L102 of the exemplary lens prescription shown in FIG. 1, wereeach split into lens sub-elements L27A and L27B, and L28A and L28B,respectively, to provide improved retardance aberration correction. Ineach case, the radius of curvature of the buried surface producedbetween the two sub-elements and the thicknesses of the two sub-elementswere varied, keeping the total element thickness fixed with respect tothe original lens element. Stated alternatively, the combined thicknessof lens sub-elements L28A and L28B of FIG. 31 is substantially the sameas the thickness of lens element L102 of FIG. 1. Element L101 of FIG. 1is split into two [110] optical sub-components L27A and L27B of FIG. 31to provide fine adjustment of the compensation. The thickness and radiusof curvature of buried surface 83 provide control over the retardanceaberrations at the center and edge of the pupil. Element L102 of FIG. 1is split into two [100] optical sub-components L28A and L28B of FIG. 31to provide fine adjustment of the azimuthal compensation. Each [100]sub-component has the same birefringence as a function of ray angle withrespect to the optical axis; only the azimuthal dependence varies withelement clocking.

[0224] Table 15 lists the radii of curvature and thicknesses of theoptical sub-elements produced by splitting components L101 and L102.TABLE 15 Crystal Axis Direction Element Front Radius Back Radius Ele-for Zero Clocking of Curvature of Curvature Thickness ment Clocking(degrees) (mm) (mm) (mm) L27A [110] −57.40 −10831.04108 154.8271117.96182 L27B [110] 68.88 154.82711 322.35847 32.03818 L28A [100] 40.25399.66226 −2608.81885 17.66426 L28B [100] 82.87 −2608.81885 −1902.3278032.33575

[0225]FIGS. 32A and 32B are graphical representations showing theretardance across the system exit pupil for the compensated systemproduced by the intrinsic birefringence and anti-reflection coatings forfield points at the center and edge of the field, respectively. As shownin FIGS. 25A and 25B, the contribution due the coatings is the sameorder of magnitude as the maximum residual retardance aberrations; thus,the choice of coating can significant effect the system performance. Adifferent coating design might require re-optimization of the lens toobtain best performance. In the uncompensated system, the contributiondue the coatings is relatively small and the bulk of the retardanceaberration is attributable to intrinsic birefringence.

[0226] RMS and maximum retardance over the exit pupil are listed inTable 16 for relative field heights of 0, 0.7, and 1.0. These includethe effects of intrinsic birefringence and the single layeranti-reflection coatings. The RMS retardance ranges from 0.0029 to0.0054 waves at λ_(o)=193.3 nm. The compensated system includes aretardance reduced in comparison to the 0.0048 to 0.0055 wave range inRMS retardance due to the anti-reflection coatings without intrinsicbirefringence effects. TABLE 16 Retardance (waves at λ_(o) = 193.3 nm)Relative Field Height RMS Maximum 0.0 0.0029 0.0144 0.7 0.0037 0.02661.0 0.0054 0.0326

[0227] The RMS and peak-to-valley wavefront error are listed in Table 17for the compensated design that includes the effects of intrinsicbirefringence. The wavefront errors are given for relative field heightsof 0, 0.7, and 1.0 in the Y direction, and are listed for two orthogonalpolarization components. The X component represents the wavefront errorfor an input polarization in the X direction assuming a linear polarizeralong the X direction at the system exit pupil. The Y componentrepresents the wavefront error for an input polarization in the Ydirection assuming a linear polarizer along the Y direction at the exitpupil. An RMS wavefront error that varies from 0.003 to 0.007 wavesacross the field is achieved. The peak-to-valley wavefront error isreduced by a factor ranging from approximately 47 to 124, compared withexemplary lenses in which all elements are [110], [100], or [111]optical elements oriented substantially identically. Thus, thisembodiment demonstrates that intrinsic birefringence effects can bereduced to a level acceptable for high numerical aperture lithography.TABLE 17 RMS Wavefront Error Peak-to-Valley Wavefront Error RelativeField (waves at λ_(o) = 193.3 nm) (waves at λ_(o) = 193.3 nm) Height XComponent Y Component X Component Y Component 0.0 0.006 0.003 0.0250.017 0.7 0.007 0.006 0.038 0.031 1.0 0.006 0.007 0.045 0.040

[0228] In FIGS. 33A, 33B, 33C, and 33D, wavefront errors are plotted atthe system exit pupil as contour maps. FIGS. 33A and 33B show contourplots of the residual wavefront error for the lens depicted in FIG. 31corresponding to an input polarization in the X direction, perpendicularto the field height, used with an exit pupil analyzer in the X directionfor the central and extreme field points, respectively. For the centralfield point, the maximum peak-to-valley optical path difference is 0.025waves at a wavelength of 193.3 nanometers, and at the extreme field, themaximum peak-to-valley optical path difference is 0.045 waves. FIGS. 33Cand 33D show contour plots of the residual wavefront error for the lensdepicted in FIG. 31 corresponding to an input polarization in the Ydirection, parallel to the field height, used with an exit pupilanalyzer in the Y direction for the central and extreme field points,respectively. For the central field point, the maximum peak-to-valleyoptical path difference is 0.017 waves at a wavelength of 193.3nanometers, and at the extreme field, the maximum peak-to-valley opticalpath difference is 0.040 waves.

[0229] The centroid distortion for the compensated design with intrinsicbirefringence, calculated based on the point spread function, and thetelecentricity error in the Y direction are listed at relative fieldheights of 0, 0.7, and 1.0 in Table 18 below. As shown, the residualdistortion in the X and Y directions is within 0.07 nm, suitable for 157nm lithography. The distortion is also significantly reduced relative tothe distortion of the nominal, uncorrected design given in Table 12.Changes in telecentricity error from the nominal design are negligible.TABLE 18 Relative Field X PSF Centroid Y PSF Centroid Y TelecentricityHeight Distortion (nm) Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.000.7 0.03 0.01 0.11 1.0 0.00 0.00 0.51

[0230] Table 19 provides a summary of Strehl ratio of the design of lens100 of FIG. 31. The Strehl ratio values are calculated at field pointscentered on the point-spread function, i.e., distortion effects were notconsidered. As shown in Table 19, an aberration free system at 0.75 NAhas a Strehl ratio of 0.8434. The performance of the nominal designwithout intrinsic birefringence effects slightly exceeds the performanceof an ideal 0.75 NA lens by 0.0004 to 0.0017.

[0231] For the compensated system with intrinsic birefringence, theStrehl ratio is similar to that of the nominal design withoutconsidering the effects of intrinsic birefringence, and relative to a0.75 NA, aberration-free system. TABLE 19 Extreme Design Layout On-AxisField 70% Field Field Aberration-free lens (0.75 NA) 0.8434 0.84340.8434 Nominal design, no 0.8439 0.8447 0.8451 birefringence Elementsaligned to compensate 0.8435 0.8430 0.8428

[0232] Embodiment 5

[0233] The fifth exemplary embodiment for application of thecompensation techniques for intrinsic birefringence may be described inconjunction with a catadioptric optical system such as a projection lensfor photolithography that employs a polarization beam splifter. Such anexemplary lens is disclosed as the second embodiment of U.S. Pat. No.6,081,382 by Y. Omura, the contents of which are herein incorporated byreference. This exemplary lens is depicted in the schematic illustrationof FIG. 34. The system advantageously operates at a central wavelengthof λ_(o)=193.3 nm and at a numerical aperture of 0.80. The image fieldis an 8×25 mm rectangular slit field and the lens provides 4×reduction.All lens elements are constructed from fused silica in the exemplaryembodiment, but other materials may be used in other exemplaryembodiments.

[0234] For an optical system employing a polarization beam splitter andutilizing polarized input radiation, it is useful to take into accountthe polarization state of the beam through different paths through thesystem. In Embodiment 5, the input polarization may be linear andoriented along the direction of the X-axis; this polarizationcorresponds to s-polarized light upon reflection at polarizationselective surface 208 of beam splitter 240. The X-axis designation isarbitrary and is defined with respect to a Cartesian coordinate systemin which the optical axis of the incoming light beam is designated theZ-direction and the X-axis is parallel to the horizontal direction. Beamsplitter 240 may be coated to maximize the reflectance of s-polarizedlight and the transmittance of p-polarized light.

[0235] The exemplary lens system includes object field 230, image field231, optical axis 248, and aperture stop 233. Beam 249 enters prism 207of beam splitter 240 on the first pass and reflects off polarizationselective surface 208 and travels through prism 207 in a downwarddirection. Upon exiting prism 207 of beam splitter 240, beam 249 travelsthrough quarter wave plate 209 and refractive element 210, reflects fromreflective surface 211 of spherical mirror 212, and returns throughrefractive element 210 and quarter wave plate 209. First quarter waveplate 209 is oriented such that the birefringence axis is at a 45° anglewith respect to the polarization orientation of beam 249 on both passes.The double pass through the wave plate and the reflection fromreflective surface 211 rotates the polarization state of the beam suchthat it is transmitted by polarization selective surface 208 on thesecond pass through beam splitter 240. Following the second pass throughprism 207, beam 249 passes through prism 213 of beam splitter 240 andsecond quarter wave plate 214 having a birefringence axis oriented at45° with respect to the polarization orientation of the beam whichconverts the polarization state to circularly-polarized. This is asdescribed in U.S. Pat. No. 6,081,382.

[0236] The root-mean-square (RMS) and maximum retardance over the exitpupil are listed in Table 20 for the nominal design without intrinsicbirefringence effects, for five positions across the 16×100 mm objectfield 230. These result from the single-layer anti-reflection coatingsused in the model and the quarter wave plates; the effects ofpolarization selective surface 208 of beam splitter 240 are alsoincluded in the model assuming perfect reflection for s-polarized lightand perfect transmission for p-polarized light. TABLE 20 Object FieldRetardance (waves at λ_(o) = 193.3 nm) (X, Y) in mm RMS Maximum (−50,−4) 0.0054 0.0274 (−35, 0) 0.0045 0.0243 (0, 0) 0.0044 0.0237 (35, 0)0.0045 0.0245 (50, 4) 0.0042 0.0233

[0237]FIGS. 35A and 35B depict the retardance across the system exitpupil due to the anti-reflection coatings and wave plates for the fieldpoints at the center and extreme corner of the field (X=50 mm and Y=4 mmat object field 230), respectively, for the exemplary lens shown in FIG.34. FIG. 35A shows that, at the center of the field, the retardance iszero at the center of the pupil and generally increases in magnitudetowards the edge of the pupil. At the extreme corner of the rectangularfield, the retardance shows a roughly constant linear component,oriented vertically across the exit pupil, as shown in FIG. 35B.

[0238]FIGS. 36A, 36B, 36C, and 36D show wavefront errors for the nominaldesign, without the effects of intrinsic birefringence, plotted at thesystem exit pupil as contour maps. FIGS. 36A and 36B show contour plotsof the residual wavefront error for the lens depicted in FIG. 34corresponding to an input polarization in the X direction used with anexit pupil analyzer in the X direction for the center and extreme cornerof the field (X=50 mm and Y=4 mm at the reticle), respectively. For thewavefront error at the central field point shown in FIG. 36A, themaximum peak-to-valley optical path difference is approximately 0.099waves at a wavelength of 193.3 nanometers, and for wavefront error atthe at the extreme field shown in FIG. 36B, the maximum peak-to-valleyoptical path difference is approximately 0.160 waves. FIGS. 36C and 36Dshow contour plots of the residual wavefront error for the lens depictedin FIG. 34 corresponding to an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the central andextreme field points, respectively. For the wavefront error at thecentral field point shown in FIG. 36C, the maximum peak-to-valleyoptical path difference is approximately 0.093 waves at a wavelength of193.3 nanometers, and for the wavefront error at the extreme field shownin FIG. 36D, the maximum peak-to-valley optical path difference isapproximately 0.152 waves.

[0239] The RMS and peak-to-valley wavefront errors are listed in Table21 below for the nominal design, without the effects of intrinsicbirefringence, at five exemplary field points. These values representthe wavefront errors at optimum focus, with tilt terms removed to locateeach image point at the center of the wavefront in the calculation.Results are given for two orthogonal polarization components. The Xcomponent represents the wavefront error assuming a linear polarizeralong the X direction at the system exit pupil, and the Y componentrepresents the wavefront error assuming a linear polarizer along the Ydirection at the exit pupil. The RMS wavefront error is shown to varyover the field from 0.011 to 0.016 waves at k=193 nm. TABLE 21 RMSWavefront Error Peak-to-Valley Wavefront Error Object Field (waves atλ_(o) = 193.3 nm) (waves at λ_(o) = 193.3 nm) (X, Y) in mm X Component YComponent X Component Y Component (−50, −4) 0.015 0.015 0.161 0.149(−35, 0) 0.016 0.016 0.157 0.162 (0, 0) 0.011 0.011 0.099 0.093 (35, 0)0.016 0.016 0.161 0.153 (50, 4) 0.015 0.015 0.160 0.152

[0240] Table 22 shows the centroid distortion for the nominal design,calculated based on the point spread function (PSF), for the same fiveexemplary field points. The maximum image distortion is approximately27.1 nm. The chief ray telecentricity error across the field is within0.4 mrad. TABLE 22 Object Field (X, Y) X PSF Centroid Y PSF Centroid inmm Distortion (nm) Distortion (nm) (−50, −4) −24.21 −3.38 (−35, 0)−27.13 −1.35 (0, 0) 0.00 −0.03 (35, 0) 27.13 1.36 (50, 4) 24.19 3.45

[0241] Catadioptric systems with a polarization selective surfacegenerally work well with a single input polarization state. Thepolarization state that is orthogonal to the design input polarizationstate is lost at the polarization selective surface. Thus, if the inputpolarization is fixed, retardance aberrations prior to the polarizationselective surface couple light out of the system, causing apodization ofthe transmitted beam, and contribute a fixed phase to the transmittedwavefront. As such, apodization is advantageously minimized to maintainefficiency and high-performance imaging. This may be achieved when theretardance aberrations prior to the polarization selective surface areeither along or orthogonal to the input polarization state. Thus forthis catadioptric embodiment, retardance aberrations are advantageouslyminimized by properly orienting and shaping lens elements after thesecond wave plate, such as second wave plate 214. For the surfaces priorto polarization selective surface 208, the component of the retardanceaberration that is neither along nor orthogonal to the designpolarization state is advantageously minimized. This approach may bemore helpful than minimizing the retardance in lens elements prior tothe polarization selective surface. Relative designations “before” and“after” are used in reference to the path of a beam traveling from theobject plane to the image plane, throughout the specification.

[0242]FIGS. 37A and 37B show the net retardance across the system exitpupil for field points at the center and extreme corner of the field(X=50 mm and Y=4 mm at the reticle), respectively, in the exemplaryembodiment in which the components preceding second wave plate 214 areassumed to have no intrinsic birefringence and in which the componentsfollowing second wave plate 214 are [110] optical elements identicallyaligned in three dimensions, in the exemplary catadioptric opticalsystem illustrated in FIG. 34, at a wavelength of 193.3 nanometers. Inthe retardance plots of FIGS. 37A, 37B and similar figures, theretardance orientation rotates by 90 degrees at one-half-wave intervals,i.e., the effect of a 0.75 wave retarder at 0 degrees is the same as a0.25 wave retarder at 90 degrees. Thus, the peak retardance due tointrinsic birefringence for the exemplary embodiment described in FIGS.37A and 37B, is approximately 0.75 waves at a wavelength of 193.3nanometers, with small variation with object field height.

[0243] In FIGS. 38A and 38B, the net retardance across the system exitpupil is depicted for field points at the center and extreme corner ofthe field, respectively, in the exemplary embodiment in which thecomponents preceding second wave plate 214 are assumed to have nointrinsic birefringence and in which the components following the secondwave plate 214 are [100] optical elements identically aligned in threedimensions in the exemplary catadioptric optical system illustrated inFIG. 34, at a wavelength of 193.3 nanometers. The peak retardance due tointrinsic birefringence in this example is approximately 0.60 waves at awavelength of 193.3 nanometers, with small variation with object fieldheight.

[0244]FIGS. 39A and 39B show the net retardance across the system exitpupil for field points at the center and extreme corner of the field,respectively, in the exemplary embodiment in which the componentspreceding second wave plate 214 are assumed to have no intrinsicbirefringence and in which the components following second wave plate214 are [111] optical elements identically aligned in three dimensionsin the exemplary catadioptric optical system illustrated in FIG. 34, ata wavelength of 193.3 nanometers. The peak retardance due to intrinsicbirefringence in this example is approximately 0.90 waves at awavelength of 193.3 nanometers.

[0245] Additional performance degradation may result from retardanceaberrations produced by elements preceding second wave plate 214. Inparticular, retardance aberrations produced by elements precedingpolarization selective surface 208 may, in general, cause light tocouple out of the system, resulting in pupil intensity non-uniformity,and this may also change the transmitted wavefront.

[0246] With elements following second quarter wave plate 214 identicallyaligned in three dimensions such that their [110], [100], or [111]crystal axes lie along optical axis 248, the intrinsic birefringenceproduces very large retardance aberrations and in turn wavefrontaberrations, as shown in the preceding figures. Without compensation,this unacceptably large aberration significantly exceeds the allowablewavefront error in high-performance photolithography, in particular,photolithography used to produce distortion-free patterns needed intoday's semiconductor manufacturing industry.

[0247] For compensating intrinsic birefringence effects in acatadioptric system such as described in the present embodiment, thereare additional considerations for optimizing the performance comparedwith compensation in an all-refractive system, such as those describedin Embodiments 3 and 4.

[0248]FIG. 40 is a schematic side view of the lens according toexemplary embodiment 5, in which each of [110] optical elements 203-206,218-220, 222-224 and 226-227A are hatched. The lens, according toexemplary embodiment 5, is substantially similar to the lens shown inFIG. 34, with the notable exception being that the refractive lenselements are advantageously oriented with respect to their crystallattices and element 227 of the lens in FIG. 34 is split into two lenselements 227A and 227B in the lens of the fifth embodiment shown in FIG.40. This exemplary catadioptric system has an NA of approximately 0.80and may advantageously be used to manufacture integrated circuits. Morespecifically, the system may be used in a lithography tool such as astepper, projection printer, or the like, used in the semiconductormanufacturing industry to produce a sequence of patterns on substratesto produce an integrated circuit or other semiconductor device.

[0249] Because polarization selective surface 208 is employed in theexemplary catadioptric system of the fifth exemplary embodiment, it isuseful to balance or minimize the retardance produced by severaldifferent groups of elements. The front group 242 of elements includesthe lens elements 201-206 preceding beam splitter 240 and the first passthrough prism 207 of beam splitter 240 up to polarization selectivesurface 208. Second group 244 comprises the second pass through prism207 of beam splitter 240 following reflection by polarization selectivesurface 208, first quarter wave plate 209, refractive lens element 210,and reflective surface 211 of spherical mirror 212, and the return pathto polarization selective surface 208 through prism 207. Third group 240comprises prism 213 of beam splitter 240 following transmission throughpolarization sensitive surface 208, second quarter wave plate 214, andelements 215 and 218-227B between the beam splitter and wafer, alsoreferred to as the image side of beam splitter 240. Elements 201-206 aredisposed on the object side of beam splitter 240.

[0250] According to an exemplary embodiment, input beam 249 is linearlypolarized in the horizontal direction, parallel to the X-axis and in thelong direction of the rectangular object field. For a given ray,depending on the orientation of the local birefringence axis of thecrystal material with respect to the input polarization, the intrinsicbirefringence generally causes the ray to split into two rays withorthogonal polarization orientations. Thus, intrinsic birefringence inthe front group 242 of elements may result in light being lost atpolarization selective surface 208, since light that is polarized in thevertical direction will be transmitted through the beam splitter ratherthan reflected. Since the birefringence magnitude and axis orientationvaries with propagation direction through the crystal, intensitynon-uniformity may result across the system exit pupil.

[0251] In the present embodiment, the linear polarization of input beam249 may be utilized to minimize the effects of intrinsic birefringencein front group 242. If a given lens element is oriented with its [110]crystal axis along the common optical axis 248 (see FIG. 5A), and thelocal birefringence axis for the ray along the optical axis is orientedhorizontally (i.e., parallel to the input polarization), rays at smallangles with respect to the optical axis correspond to extraordinaryrays, and very little energy will couple into the vertical polarizationstate.

[0252] Similarly, if the element is oriented with its [110] crystal axisalong common optical axis 248 and the local birefringence axis along theoptical axis is oriented vertically, that is, perpendicular to the inputpolarization, rays at small angles with respect to the optical axiscorrespond to ordinary rays, and very little energy will couple into thehorizontal polarization state.

[0253] For a [100] optical element, the birefringence magnitude iscomparatively small for rays at small angles with respect to the opticalaxis. The lens elements may be aligned such that the birefringence lobesare at azimuthal angles of 0, 90, 180, and 270° (see FIG. 5B) in orderto minimize the component of the retardance that is neither parallel nororthogonal to the input polarization state.

[0254] In this embodiment, the crystal lattice orientations of theelements in front group 242 are selected from the three crystal latticeorientations to minimize both the horizontal and vertical variation inretardance. According to other exemplary embodiments of similarcatadioptric systems, and in which circular input polarization is used,and a quarter wave plate is employed immediately prior to the beamsplitter to convert the polarization of the beam to linearly-polarizedlight, the optical elements may advantageously be clocked to minimizethe RMS retardance, or produce circular residual retardance aberrationsto match the input polarization state.

[0255] Still referring to FIG. 40, the first two lens elements 201 and202 are [100] optical elements, clocked to have birefringence lobesoriented at azimuthal angles of 0, 90, 180, and 270° in the exemplaryembodiment. Lens elements 203, 204, 205, and 206 are oriented so thatthe optical axis is along their [110] lattice directions, with relativeclockings of 0, 90, 90, and 0°, with respect to an orientation thatgives a horizontal birefringence axis along the optical axis.

[0256] Prism 207 of beam splitter 240 is oriented such that its [100]crystal axis lies along optical axis 248 for the first pass of inputbeam 249, again with birefringence lobes oriented at azimuthal angles of0, 90, 180, and 270°. Upon reflection from the 45° polarizationselective surface 208, the beam maintains an equivalent directionthrough the crystal. According to another embodiment, beam splitter 240may be a polarization beam splitter formed of a cubic crystallinematerial and aligned such that its [110] lattice direction liessubstantially along optical axis 248 and the local birefringence axisfor the ray entering the beam splitter along the optical axis isoriented horizontally, parallel to the input polarization orientation,such that upon reflection from the 45° polarization selective surface208, the beam maintains an equivalent direction through the crystal.

[0257] The RMS and maximum retardance over the exit pupil are listed inTable 23 for five positions across object field 230; these include theeffects of intrinsic birefringence in the elements 201-206 precedingbeam splitter 240 and segment 207 of beam splitter 240 up to thereflective surface 211 of spherical mirror 212, as well as retardancedue to the single-layer anti-reflection coatings used in the model. Theeffects of the quarter wave plates and polarization selective surface ofthe beam splitter are not included. TABLE 23 X Object Field Y ObjectField Retardance (waves at λ_(o) = 193.3 nm) Height (mm) Height (mm) RMSMaximum −50 −4 0.0135 0.0799 −35 0 0.0155 0.0681 0 0 0.0087 0.0350 35 00.0138 0.0617 50 4 0.0096 0.0604

[0258]FIGS. 41A and 41B depict the retardance across the system exitpupil due to the intrinsic birefringence of front group 242 andanti-reflection coatings for the field points at the center and extremecorner of the field (X=50 mm and Y=4 mm at the reticle), respectively.FIG. 41A shows that, at the center of the field, the retardance is zeroat the center of the pupil and increases in magnitude towards the edgeof the pupil. At the outer corner of the field, FIG. 41B shows that theretardance includes a linear component, oriented roughly horizontallyover the pupil.

[0259] For the center of the field, the system transmittance varies froma normalized value of 1.0 at the center of the pupil to a minimum valueof approximately 0.930 at the edge of the pupil. For the extreme orouter corner of the field, the normalized system transmittance variesfrom 1.0 at the center of the pupil, to a minimum of approximately 0.915at the edge of the pupil. In the second group 244 of elements, in whichthe beam reflects off reflective surface 211 and returns to polarizationselective surface 208 of beam splitter 240, there are relatively fewerdegrees of freedom for minimizing the retardance. In this element group,therefore, each individual lens element component may be aligned withits [100] crystal axis along the optical axis, with peak birefringencelobes oriented at azimuthal angles of 0, 90, 180, and 270°. Thisminimizes the component of the retardance that is neither parallel nororthogonal to the axis of the polarization selective surface. Becausethe ray angles are relatively small with respect to the optical axis(within 11° from the optical axis) and the birefringence lobes in thebeam splitter path are preferentially oriented, the effects of theintrinsic birefringence are minimized.

[0260] After transmission through polarization selective surface 208 ofthe beam splitter, prism 213 of beam splitter 240 is also oriented to bea [100] optical element and oriented to have birefringence lobes at 0,90, 180, and 270°, to minimize the effects of the intrinsicbirefringence since ray angles are small with respect to the opticalaxis (within 6°) and the birefringence lobes are again preferentiallyoriented.

[0261] According to another embodiment, prism 213 of beam splitter 240may be aligned such that its [110] lattice direction lies substantiallyalong optical axis 248 and the local birefringence axis for the raytraveling along the optical axis and entering prism 213 is substantiallyperpendicular to the polarization direction of the ray; this embodimentmay be used in conjunction, for example, with a cubic crystalline prism207 oriented such that its [110] lattice direction lies substantiallyalong optical axis 248 and the local birefringence axis for the inputray traveling along the optical axis is substantially parallel to theinput polarization direction, to minimize net retardance.

[0262] In the present embodiment, beam splitter 240 may be oriented suchthat the input beam is polarized horizontally, corresponding tos-polarized light at the polarization selective surface 208, andpolarization selective surface 208 is coated to preferentially reflects-polarized light. In other exemplary embodiments, the beam splitter maybe designed to transmit the beam on the first pass through the beamsplitter and reflect the beam on the second pass, and the crystalorientations of the segments would again be selected to minimize netretardance and maintain an equivalent lattice direction along theoptical axis upon reflection.

[0263] Third group 246 includes elements 213-227B. For the third group246 of elements, compensation of the retardance produced by theintrinsic birefringence is again achieved by selective orientation ofthe crystal axis alignment for each lens element with respect to theoptical axis, the relative rotations of those elements about the opticalaxis, and by splitting last element 227 of the exemplary lens embodimentshown in FIG. 34, into two sub-elements 227A and 227B that provide thesame total thickness and power but include individual thicknesses and acurvature of buried surface 250 between them that is optimized tominimize retardance. As in the previous embodiments, a combination of[110] and [100] optical elements are utilized to allow the retardancecontributions of the individual elements in third group 246 of elementsto be balanced, thereby correcting for intrinsic birefringence andreducing retardance.

[0264] In this embodiment, elements 215, 221, and 225 and quarter waveplates 209 and 214 are [100] optical elements oriented such that thepeak birefringence lobes are oriented at azimuthal angles of 0, 90, 180,and 270°. Also, the two sub-elements include first sub-element 227Aoriented with its [110] crystal axis along optical axis 248 and secondsub-element 227B with its [100] crystal axis along optical axis 248. Thecrystal axis orientation and clockings of each of the components aregiven in Table 24 below. The table includes refractive lens elements201-206, 210, 215, 218-226 and 227A and 227B, beam splitter prisms 207and 213 and wave plates 209 and 214. For [110] optical elements, theclocking of each element is given relative to an orientation thatproduces peak birefringence along the optical axis that is oriented withthe retardance axis substantially parallel to the X axis (horizontal, inthe long direction of the specified field of view). For [100] opticalelements, the clocking of each element is given relative to anorientation that produces peak birefringence lobes in the X-Z and Y-Zplanes, at azimuthal angles of 0, 90, 180, and 270°. TABLE 24 CrystalAxis Direction Element Clocking Element along Optical Axis (degrees) 201[100] 0 202 [100] 0 203 [110] 0 204 [110] 90 205 [110] 90 206 [110] 0Prism 207, Segment 1 [100] 0 Prism 207, Segment 2 [100] 0 Wave Plate209, Pass 1 [100] 0 210, Pass 1 [100] 0 210, Pass 2 [100] 0 Wave Plate209, Pass 2 [100] 0 Prism 207, Segment 3 [100] 0 Prism 213, Segment 4[100] 0 Wave Plate 214 [100] 0 215 [100] 126.80 218 [110] 51.77 218,toroidal rear surface S2 — −30.00 219 [110] 149.94 220 [110] −81.22 221[100] 179.17 222 [110] −0.27 223 [110] 60.98 224 [110] 45.86 225 [100]−69.14 226 [110] 90.29   227A [110] −30.24   227B [100] 11.80

[0265] RMS and maximum retardance over the exit pupil are listed inTable 25 below for five exemplary field positions and include theeffects of intrinsic birefringence for the elements following the secondquarter wave plate 214 and the single layer anti-reflection coatingsused in the model. The RMS retardance ranges from 0.0062 to 0.0084 wavesat λ_(o)=193.3 nm, across the field. TABLE 25 X Object Field Y ObjectField Retardance (waves at λ_(o) = 193.3 nm) Height (mm) Height (mm) RMSMaximum −50 −4 0.0084 0.0518 −35 0 0.0078 0.0473 0 0 0.0062 0.0390 35 00.0078 0.0473 50 4 0.0084 0.0518

[0266]FIGS. 42A and 42B depict the retardance across the system exitpupil for field points at the center and extreme corner of the field(X=50 mm and Y=4 mm at the reticle), respectively, for the compensatedsystem as detailed in Table 24, produced by the intrinsic birefringenceof the group of elements following second wave plate 214 (in third group246) and also due to anti-reflection coatings.

[0267] The total RMS and maximum retardance over the exit pupil arelisted in Table 26 for five indicated field positions, including theeffects of intrinsic birefringence for all elements and the single layeranti-reflection coatings used in the model. RMS retardance ranges from0.0076 to 0.0123 waves at λ_(o)=193.3 nm. In one embodiment, RMSretardance may be minimized in the group of elements following thesecond wave plate, rather than the total retardance. Such reduction ofretardance may sufficiently lower levels of retardance for the overallsystem, without the necessity of performing the same optimization on allelement groups. TABLE 26 X Object Field Y Object Field Retardance (wavesat λ_(o) =193.3 nm) Height (mm) Height (mm) RMS Maximum −50 −4 0.01230.0824 −35 0 0.0105 0.0689 0 0 0.0076 0.0493 35 0 0.0113 0.0733 50 40.0130 0.0828

[0268]FIGS. 43A and 43B are graphical representations depicting theretardance across the system exit pupil produced by the intrinsicbirefringence of all elements and anti-reflection coatings for fieldpoints at the center and corner of the field (X=50 mm and Y=4 mm at thereticle), respectively, for the compensated system, as detailed in Table24.

[0269] Similar to the refractive example of Embodiment 3, surface S2 ofrefractive optical element 218 immediately preceding aperture stop 233,is a toroidal surface in which the radius of curvature in orthogonaldirections is varied along with the clocking of the surface tocompensate for astigmatism due to variations in average index ofrefraction. The radii of curvature for the toroidal surface are listedin Table 27 below, and the local X- and Y-axes of the surface arerotated by −30° about the optical axis relative to the system X- andY-axes. TABLE 27 Surface Radius of Curvature (mm) 218, Surface S2, localX direction 1543.4724 218, Surface S2, local Y direction 1543.4659

[0270] The fifth exemplary embodiment also illustrates that finalelement 227 of the exemplary lens shown in FIG. 34 and based on a knownlens prescription, was split into sub-elements 227A and 227B shown inFIG. 40, to provide improved retardance aberration correction. Theradius of curvature of the buried surface 250 between the elements andthe thicknesses of the two segments were varied, keeping the totalelement thickness unchanged with respect to single element 227. Table 28provides the radius of curvature and thicknesses of the two segments.TABLE 28 Crystal Axis Front Direction Element Radius of Back Radius forZero Clocking Curvature of Curvature Thickness Element Clocking(degrees) (mm) (mm) (mm) 227A [110] −30.24 92.4548 263.3382 47.9615 227B[100] 11.80 263.3382 −4239.8801 5.0385

[0271]FIGS. 44A, 44B, 44C, and 44D are contour plots of wavefront errorsplotted at the exit pupil for the optical system illustrated in FIG. 40.FIGS. 44A and 44B are contour plots of the residual wavefront errorcorresponding to an input polarization in the X direction used with anexit pupil analyzer in the X direction for the center and extreme cornerof the field (X=50 mm and Y=4 mm at the reticle), respectively. For thewavefront error at the central field point shown in FIG. 44A, themaximum peak-to-valley optical path difference is approximately 0.125waves at a wavelength of 193.3 nanometers, and for wavefront error atthe at the extreme field shown in FIG. 44B, the maximum peak-to-valleyoptical path difference is approximately 0.191 waves. FIGS. 44C and 44Dare contour plots of the residual wavefront error corresponding to aninput polarization in the Y direction used with an exit pupil analyzerin the Y direction for the central and extreme field points,respectively. For the wavefront error at the central field point shownin FIG. 44C, the maximum peak-to-valley optical path difference isapproximately 0.117 waves at a wavelength of 193.3 nanometers, and forthe wavefront error at the extreme field shown in FIG. 44D, the maximumpeak-to-valley optical path difference is approximately 0.192 waves.

[0272] The RMS and peak-to-valley wavefront errors are listed in Table29 for the compensated design, including the effects of intrinsicbirefringence, at five field points. These values represent thewavefront errors at optimum focus, but tilt terms have been removed tolocate each image point at the center of the point-spread function.Results are given for two orthogonal polarization components. The Xcomponent represents the wavefront error assuming a linear polarizeralong the X direction at the system exit pupil, and the Y componentrepresents the wavefront error assuming a linear polarizer along the Ydirection at the exit pupil. TABLE 29 Peak-to-Valley RMS Wavefront ErrorWavefront Error (waves at λ_(o) = 193.3 nm) (waves at λ_(o) = 193.3 nm)Object Field X Y X Y (X, Y) in mm Component Component ComponentComponent (−50, −4) 0.018 0.016 0.185 0.189 (−35, 0) 0.019 0.017 0.1760.180 (0, 0) 0.012 0.011 0.125 0.117 (35, 0) 0.018 0.017 0.177 0.184(50, 4) 0.018 0.016 0.191 0.192

[0273] Table 29 shows that the RMS wavefront error varies across thefield from 0.011 to 0.019 waves at λ=193 nm. This is comparable to therange of 0.011 to 0.016 waves described in Table 21 for the nominaldesign embodiment calculated without considering the effects ofintrinsic birefringence The maximum change in RMS wavefront error fromthe nominal design embodiment calculated without considering the effectsof intrinsic birefringence is 0.003 waves. It can be seen that asignificant compensation for wavefront errors caused by intrinsicbirefringence has been achieved by the techniques of the presentinvention. For comparison, according to a comparative exemplaryembodiment in which all elements following the second wave plate are[110] optical elements oriented with the same three-dimensional crystallattice directions, the peak retardance is approximately 0.75 waves, asshown in FIGS. 37A and 37B. The maximum peak-to-valley wavefront errorfor the compensated design with intrinsic birefringence is 0.192 waves,which is comparable to the maximum peak-to-valley wavefront error of0.162 waves for the nominal design without intrinsic birefringence.

[0274] Table 30 shows the centroid distortion for the exemplaryembodiment in which the effects of intrinsic birefringence arecompensated for, as described above. This centroid distortion iscalculated based on the point spread function and is listed for fiveexemplary field points. The maximum image distortion is approximately−38.5 nm, and the maximum change in distortion from the nominal designis approximately −13.8 nm. Distortion was not considered in thisembodiment, but further design variables, such as discussed inconjunction with Embodiments 3 and 4 may be used to balance changes indistortion due to the intrinsic birefringence effects in the compensatedsystem. The chief ray telecentricity error across the field is within0.4 mrad and changes in chief ray telecentricity error are negligible.TABLE 30 Object Field (X, Y) X PSF Centroid Y PSF Centroid in mmDistortion (nm) Distortion (nm) (−50, −4) −38.01 −5.48 (−35, 0) −38.53−1.18 (0, 0) −0.11 −0.05 (35, 0) 38.26 1.13 (50, 4) 37.70 5.53

[0275] Table 31 provides a summary of the performance of the exemplarysystem in terms of the Strehl ratio. Strehl ratio values in Table 31 arecalculated at field points centered on the wavefront in the exit pupil(i.e., wavefront distortion effects were removed).

[0276] As shown in Table 31, an aberration free system has a Strehlratio of 0.8178 at a numerical aperture of 0.80. For the nominal designwithout intrinsic birefringence effects considered, the Strehl ratio isreduced by a maximum value of 0.0084. For the compensated system withintrinsic birefringence, the Strehl ratio is reduced from that of anaberration free system by a maximum value of 0.0151. TABLE 31 ObjectField (X, Y) in mm Design Layout (−50, −4) (−35, 0) (0, 0) (35, 0) (50,4) Aberration free lens 0.8178 0.8178 0.8178 0.8178 0.8178 (0.80 NA)Nominal, no 0.8102 0.8096 0.8134 0.8094 0.8101 birefringence consideredElements aligned to 0.8056 0.8063 0.8110 0.8045 0.8027 compensate

[0277] Also as described in conjunction with previous embodiments, oneor more stress birefringent elements, wave plates, or combinationsthereof may additionally be used to correct for residual birefringencevariation and constant residual retardance which remains in thecatadioptric system after the above-described system corrections havebeen made.

[0278] Referring again to FIG. 40, according to yet another exemplaryembodiment, stress may be applied to a reflective element such as mirrorsurfaces 211 or 216 to alter the base radius of curvature in orthogonaldirections. This stress may correct for residual astigmatism in theexemplary catadioptric optical system. As described in conjunction withembodiment three, the use of at least one optical element whose baseradius of curvature differs in orthogonal directions may additionally oralternatively be used to compensate for residual astigmatism due tovariations in the average index of refraction in the cubic crystallineoptical elements.

[0279] According to other exemplary catadioptric embodiments, some ofthe lens elements may be formed of non-cubic crystalline material oradditional lens elements formed of non-cubic crystalline material may beused. Various suitable non-cubic crystalline materials such as dry fusedsilica may be used.

[0280] According to still other catadioptric embodiments, the principlesof the present invention may be applied to catadioptric systems that donot include beam splitters or wave plates, such as described in U.S.Pat. No. 6,195,213 B1 to Omura et al., the contents of which are herebyincorporated by reference.

[0281] In summary, embodiment five demonstrates that the principles ofthe present invention may be applied to a catadioptric optical system tosignificantly reduce intrinsic birefringence effects and systemretardance, to levels acceptable for high numerical aperturelithography.

[0282] Embodiment 6

[0283]FIG. 45 shows an exemplary arrangement of an optical system usedto demonstrate the basic technique for mitigating the effects ofintrinsic birefringence using an element including a stress-inducedbirefringence. This illustrated optical system consists of two cubiccrystalline optical elements concentric about focal point 310 of aconverging beam. The beam passes through two cubic crystalline elements302 and 306 whose radii of curvature are specified to be concentric withfocal point 310. Cubic crystalline optical elements 302 and 306 havethicknesses 304 and 308, respectively. In an exemplary embodiment, eachof thicknesses 304 and 308 may be 5 mm and cubic crystalline elements302 and 306 may be assumed to have a birefringence magnitude,n_(e)−n_(o), of −12×10⁻⁷, corresponding to the intrinsic birefringenceof calcium fluoride measured at a wavelength of 157 nm. Cubiccrystalline optical elements 302 and 306 may each be [110] cubiccrystalline optical elements aligned along common optical axis 312, witha relative clocking of 90 degrees about optical axis 312. According toother exemplary embodiments, the relative clocking of the elements mayvary, the crystal orientation of the elements may vary, and additionalelements may be included.

[0284] First optical element 302 includes a compressive hoop stress ofapproximately 19 lbs./in² applied around the perimeter of the element tominimize net RMS retardance of the system. Various techniques may beused to stress the element, and tensile and compressive stresses ofvarious other magnitudes may be used in other exemplary embodiments.

[0285]FIG. 46A is a graphical representation depicting the individualretardance contribution due to the stress-induced birefringence of firstelement 302 and excluding the effects of intrinsic birefringence. FIG.46A includes a peak retardance of 0.0142 waves and RMS retardance of0.0047 waves.

[0286]FIG. 46B depicts the net retardance for optical system of thisexemplary embodiment including the stress-induced birefringence, andshows a maximum residual retardance of 0.0186 waves and RMS retardanceof 0.0065 waves. The resulting retardance variation over the pupil shownin FIG. 46B is similar to the retardance variation given in FIG. 9C as aresult of the addition of a 2.3 mm thick [100] cubic crystalline thirdoptical element. According to the embodiment using the stress-inducedbirefringence, the maximum peak and RMS net retardance values arecomparable to the respective values of 0.0139 and 0.0041 waves for theembodiment described in FIG. 9C. In this manner, stress-inducedbirefringence applied to one of the [110] optical elements is shown toprovide similar correction as the addition of a [100] cubic crystallineelement.

[0287] Such application of stress-induced birefringence to a [110]optical element of an exemplary optical system including two [110]optical elements, is intended to be exemplary only. The stress-inducedbirefringence may be applied to the other [110] optical element 306 inanother exemplary embodiment. Furthermore, this technique may beadvantageously applied to various other optical systems includingvarious numbers of elements clocked at various angles with respect toone another. The stress-induced birefringence may be applied to [100],[111] or non-cubic crystalline optical elements such as dry fusedsilica, for example. According to one exemplary embodiment, a third,non-birefringent element may be added to the arrangement shown in FIG.45 (such as the arrangement shown in FIG. 6, for example) and thestress-induced birefringence may be applied thereto.

[0288] The previously-described method for measuring or using computermodeling to determine the retardance of an optical system, identifyingan optical element or elements to have stress-induced birefringenceapplied thereto, then applying the compressive or tensile stress as ahoop or other stress to the identified optical element, may be likewiseused in the present embodiment, to produce stress-induced birefringenceas described above, and to reduce residual retardance.

[0289] The principles described in embodiment 6, may be applied to thepreviously described exemplary lens systems. In particular,stress-induced birefringence may be applied to the illustrated elementsor additional elements added to the illustrated embodiments.

[0290] The preceding six exemplary embodiments are intended to beillustrative, not restrictive of the present invention. Furthermore, itis intended that the various exemplary techniques for compensating theeffects of intrinsic birefringence, including retardance aberrations,wavefront aberrations produced by variations in average index ofrefraction, and variations in system transmittance, described inconjunction with one of the exemplary embodiments, may also be appliedto the other exemplary embodiments. For example, the selection ofmultiple [110] optical elements together with at least one [100] opticalelement, the relative clocking of the elements, [111] optical elements,stress-induced birefringent elements with radially varying stress,stress induced birefringent elements with stress varying along axesperpendicular to the optical axis, the selection of various other lensorientations, the optimization of lens element thicknesses, spacings,radii of curvature and aspheric coefficients, and the other exemplarytechniques and elements may be used to correct for intrinsicbirefringence in the various exemplary optical systems. Similarly,another aspect of the present invention—the method for compensating forresidual astigmatism due to variations in the average index ofrefraction in the cubic crystalline optical elements, through the use ofat least one optical element whose base radius of curvature differs inorthogonal directions, may be used in any of the previous embodiments.

[0291] The preceding merely illustrates the principles of the invention.It will thus be appreciated that those skilled in the art will be ableto devise various arrangements which, although not explicitly describedor shown herein, embody the principles of the invention and are includedwithin its scope and spirit. Furthermore, all examples and conditionallanguage recited herein are principally intended expressly to be onlyfor pedagogical purposes and to aid in understanding the principles ofthe invention and the concepts contributed by the inventors tofurthering the art, and are to be construed as being without limitationto such specifically recited examples and conditions. Moreover, allstatements herein reciting principles, aspects, and embodiments of theinvention, as well as specific examples thereof, are intended toencompass both structural and the functional equivalents thereof.Additionally, it is intended that such equivalents include bothcurrently known equivalents and equivalents developed in the future,i.e., any elements developed that perform the same function, regardlessof structure. The scope of the present invention, therefore, is notintended to be limited to the exemplary embodiments shown and describedherein. Rather, the scope and spirit of the present invention isembodied by the appended claims.

We claim:
 1. An optical system including at least two cubic crystallineoptical elements aligned along a common optical axis and having theirrespective crystal lattices rotated with respect to each other and aboutsaid optical axis to reduce retardance within said optical system, andat least one compensatory [100] cubic crystalline optical elementaligned with its [100] lattice direction along said common optical axis,each compensatory [100] cubic crystalline optical element oriented toreduce retardance at locations off said optical axis, within saidoptical system.
 2. The optical system as in claim 1, in which said atleast two cubic crystalline optical elements are [111] optical elementsaligned with the same crystal lattice direction along said commonoptical axis.
 3. The optical system as in claim 1, wherein said at leasttwo cubic crystalline optical elements are aligned with their respective[111] crystal lattice directions along said common optical axis.
 4. Theoptical system as in claim 1, in which said at least two cubiccrystalline optical elements produce a net optical system retardancethat is less than the net optical system retardance when respectivethree-dimensional crystal lattices of each of said at least two cubiccrystalline optical elements are oriented substantially identically. 5.The optical system as in claim 1, in which said at least two cubiccrystalline optical elements are formed of the same material.
 6. Theoptical system as in claim 1, wherein each of said at least onecompensatory [100] cubic crystalline optical element and said at leasttwo cubic crystalline optical elements, are formed of the same material.7. The optical system as in claim 1, in which each of said at least twocubic crystalline optical elements is formed of calcium fluoride.
 8. Theoptical system as in claim 1, further comprising a stress birefringentelement aligned along said common optical axis to compensate for systemretardance.
 9. The optical system as in claim 8, wherein said stressbirefringent element comprises a powered element with a constantbirefringence magnitude.
 10. The optical system as in claim 9, whereinsaid stress birefringent element one of a) is formed of a uniaxialcrystalline material, and b) includes stress-induced birefringence. 11.The optical system as in claim 8, wherein said stress birefringentelement comprises a stressed element having a birefringence varying oneof linearly and quadratically therethrough.
 12. The optical system as inclaim 8, wherein said stress birefringent element includes a stressbirefringence magnitude that varies along an axis that is orthogonal tosaid optical axis.
 13. The optical system as in claim 1, furthercomprising a wave plate disposed along said common optical axis toreduce retardance within said optical system.
 14. The optical system asin claim 13, wherein said wave plate one of a) is formed of a uniaxialcrystalline material, and b) includes stress-induced birefringence. 15.The optical system as in claim 1, further comprising further opticalelements aligned along said common optical axis.
 16. The optical systemas in claim 15, in which at least one of said further optical elementsis formed of non-cubic crystalline material.
 17. The optical system asin claim 15, in which at least one of said at least two cubiccrystalline optical elements, said at least one compensatory [100] cubiccrystalline optical element, and said further optical elements, includesa surface with an asymmetric variation in curvature.
 18. The opticalsystem as in claim 17, in which said surface comprises a toroidalsurface.
 19. The optical system as in claim 17, in which said at leastone of said at least two cubic crystalline optical elements, said atleast one compensatory [100] cubic crystalline optical element, and saidfurther optical elements including a surface with an asymmetricvariation in curvature, is positioned to reduce astigmatism of saidoptical system due to variation in index of refraction.
 20. The opticalsystem as in claim 15, in which said further optical elements include asufficient number of further [100] cubic crystalline optical elements tocompensate for non-rotationally symmetric defects in said opticalsystem, at least one of said further [100] cubic crystalline opticalelements rotated with respect to another one of said further [100] cubiccrystalline optical elements.
 21. The optical system as in claim 1, inwhich said at least one compensatory [100] cubic crystalline opticalelement includes at least two compensatory [100] cubic crystallineoptical elements being rotated about said optical axis with respect toone another to minimize net retardance in said optical system.
 22. Theoptical system as in claim 1, in which said optical system is acatadioptric system further including at least one reflective surface.23. The optical system as in claim 22, in which one of said reflectivesurfaces includes an asymmetrical stress applied thereto to reduceastigmatism.
 24. The optical system as in claim 22, wherein saidcatadioptric system further comprises a polarization beam splitterformed of a cubic crystalline material and including a [100] latticedirection aligned substantially along said common optical axis and suchthat peak birefringence lobes of said beam splitter are one ofsubstantially perpendicular and substantially parallel to an inputpolarization direction of light provided to said optical system.
 25. Theoptical system as in claim 22, wherein said catadioptric system furthercomprises a polarization beam splitter formed of a cubic crystallinematerial and including a [110] lattice direction aligned substantiallyalong said common optical axis and such that the peak birefringence lobeof said beam splitter along said optical axis is one of substantiallyperpendicular and substantially parallel to an input polarizationdirection of polarized light provided to said optical system.
 26. Theoptical system as in claim 22, further including a light source, a beamsplitter, at least one wave plate, an object side, and an image side ofsaid optical system, and in which said at least two cubic crystallineoptical elements are positioned on said object side of said beamsplitter.
 27. The optical system as in claim 26, in which said at leasttwo cubic crystalline optical elements are [111] cubic crystallineoptical elements aligned with their respective [111] crystal latticedirections along said common optical axis, and further comprising atleast two further [111] cubic crystalline optical elements and at leastone further [100] cubic crystalline optical element on said image sideof said beam splitter, each further [111] cubic crystalline opticalelement aligned with its [111] lattice direction along said opticalaxis, and each further [100] cubic crystalline optical element alignedwith its [100] lattice direction along said optical axis, and orientedto reduce system retardance.
 28. The optical system as in claim 22,further including a light source, a beam splitter, at least one waveplate, an object side, and an image side of said optical system, and inwhich said at least two cubic crystalline optical elements and said atleast one compensatory [100] cubic crystalline optical element, arepositioned on said image side of said beam splitter.
 29. The opticalsystem as in claim 22, further comprising at least one further opticalelement aligned along said common optical axis and including astress-induced birefringence applied to reduce retardance variationwithin said optical system.
 30. The optical system as in claim 1,further comprising a light source and a mask pattern positioned suchthat said light source is capable of projecting said mask patternthrough said optical system.
 31. The optical system as in claim 30,wherein said light source comprises an excimer laser.
 32. Aphotolithography tool including the optical system as in claim
 1. 33.The photolithography tool as in claim 32, further comprising condenseroptics, a mask pattern formed on one of a reticle and a photomask, asubstrate and a light source, said photolithography tool configured toproject said mask pattern onto said substrate through said opticalsystem.
 34. A photolithography tool including the optical system as inclaim
 22. 35. An optical system including at least two cubic crystallineoptical elements aligned along a common optical axis and having theirrespective crystal lattices rotated with respect to each other and aboutsaid optical axis to reduce retardance within said optical system, andat least one compensatory [100] cubic crystalline optical elementaligned with its [100] lattice direction along said common optical axis,each compensatory [100] cubic crystalline optical element oriented toreduce retardance for light traveling at an angle with respect to saidoptical axis.
 36. An optical system including at least two [111] cubiccrystalline optical elements aligned with their respective [111] latticedirections along a common optical axis and having their respectivecrystal lattices rotated with respect to each other and about saidoptical axis to reduce retardance within said optical system, and atleast one [100] cubic crystalline optical element aligned with its [100]lattice direction along said common optical axis, each [100] cubiccrystalline optical element oriented to reduce retardance at locationsoff said optical axis, within said optical system.
 37. The opticalsystem as in claim 36, in which said [111] cubic crystalline opticalelements are oriented such that peak intrinsic birefringence lobes ofsaid respective [111] cubic crystalline optical elements are rotatedwith respect to each other.
 38. The optical system as in claim 36,wherein each [100] cubic crystalline optical element and each of said atleast two [111] cubic crystalline optical elements, are formed of thesame material.
 39. The optical system as in claim 36, in which each ofsaid [111] cubic crystalline optical elements is formed of calciumfluoride.
 40. The optical system as in claim 36, in which said opticalsystem is a catadioptric system further including at least onereflective surface.
 41. The optical system as in claim 36, furthercomprising further optical elements aligned along said common opticalaxis.
 42. The optical system as in claim 41, in which at least one ofsaid further optical elements is formed of non-cubic crystallinematerial.
 43. The optical system as in claim 41, wherein one of saidfurther optical elements comprises a further [111] cubic crystallineoptical element aligned with its [111] crystal lattice direction alongsaid common optical axis, said at least two [111] cubic crystallineoptical elements each having a first intrinsic birefringence magnitudeand said further [111] cubic crystalline optical element having a secondintrinsic birefringence magnitude that is opposite in sign to said firstintrinsic birefringence magnitude, said further [111] cubic crystallineoptical element and said at least two [111] cubic crystalline opticalelements oriented to reduce retardance within said optical system. 44.The optical system as in claim 41, in which at least one of said [111]cubic crystalline optical elements, said at least one [100] cubiccrystalline optical element, and said further optical elements, includesa stress-induced birefringence to compensate for residual retardance ofsaid optical system.
 45. The optical system as in claim 44, wherein saidstress-induced birefringence varies radially.
 46. The optical system asin claim 36, further comprising a stress birefringent element alignedalong said common optical axis to compensate for system retardance,wherein said stress birefringent element comprises a powered elementwith a constant birefringence magnitude and one of a) is formed of auniaxial crystalline material, and b) includes stress-inducedbirefringence.
 47. A photolithography tool including the optical systemas in claim
 36. 48. An optical system including at least two [111] cubiccrystalline optical elements aligned with their respective [111] latticedirections along a common optical axis and having their respectivecrystal lattices rotated with respect to each other and about saidoptical axis to reduce retardance within said optical system, and atleast one [100] cubic crystalline optical element aligned with its [100]lattice direction along said common optical axis, each [100] cubiccrystalline optical element oriented to reduce retardance for lighttraveling at an angle with respect to said optical axis.
 49. A methodfor reducing retardance in an optical system comprising: providing alens system having a lens prescription and including a plurality oforiginal optical elements aligned along a common optical axis, said lenssystem having a first net retardance; and splitting at least one of saidoriginal optical elements into two [111] sub-elements while maintainingsaid lens prescription, each of said two [111] sub-elements formed of acubic crystalline material and aligned such that their respective [111]cubic crystal lattice directions are along said optical axis, said two[111] sub-elements having their respective crystal lattices oriented toproduce a reduced net retardance being less than said first netretardance.
 50. A method for reducing retardance in an optical systemcomprising: providing a plurality of optical elements including at leasttwo first cubic crystalline optical elements and at least one [100]cubic crystalline optical element; aligning said plurality of opticalelements along a common optical axis, said at least two first cubiccrystalline optical elements aligned with the same of their respectivecrystal lattice directions along said common optical axis, and each ofsaid at least one [100] cubic crystalline optical element aligned withits respective [100] crystal axis along said common optical axis; androtating at least one of said first cubic crystalline optical elementsabout said optical axis to produce a reduced retardance with respect toa system retardance produced when the three-dimensional crystal latticesof each of said first cubic crystalline optical elements are orientedsubstantially identically; and orienting said [100] cubic crystallineoptical element to reduce off-axis retardance variation within saidoptical system.
 51. The method as in claim 50, in which said at leasttwo first cubic crystalline optical elements are [111] optical elementsaligned with their respective [111] crystal axes along said commonoptical axis.
 52. An optical system including at least two [111] cubiccrystalline optical elements aligned with their respective [111] latticedirections along a common optical axis and having their respectivecrystal lattices rotated with respect to each other and about saidoptical axis to reduce retardance within said optical system, and afurther optical element aligned along said common optical axis andincluding a stress-induced birefringence to compensate for residualretardance of said [111] cubic crystalline optical elements.
 53. Theoptical system as in claim 52, in which said further optical element isformed of a non-cubic crystalline material.
 54. The optical system as inclaim 52, in which said stress-induced birefringence varies radiallywithin said further optical element.
 55. An optical system including atleast two cubic crystalline optical elements aligned along a commonoptical axis and having the same of their respective crystal latticedirections aligned along said common optical axis and further havingtheir respective crystal lattices rotated with respect to each other andabout said common optical axis to reduce retardance within said opticalsystem, at least one of said cubic crystalline optical elementsincluding a stress-induced birefringence to compensate for residualretardance variations.
 56. The optical system as in claim 55, whereinsaid at least two cubic crystalline optical elements are [111] cubiccrystalline optical elements aligned with their respective [111] crystallattice directions along said common optical axis.
 57. The opticalsystem as in claim 56, in which said stress-induced birefringenceincreases in magnitude from center to edge.
 58. A photolithography toolincluding the optical system as in claim
 55. 59. The photolithographytool as in claim 58, further comprising further optical elements alignedalong said common optical axis, condenser optics, a mask pattern formedon one of a reticle and a photomask, a substrate and a light source,said photolithography tool configured to project said mask pattern ontosaid substrate through said optical system.